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[ x/(3+x) * (2+x)/(3+x) ] / (1-x)/(3+x) = 0,2336

 Aug 9, 2014

Best Answer 

 #1
avatar+118702 
+10

[ x/(3+x) * (2+x)/(3+x) ] / (1-x)/(3+x) = 0,2336

[x/(3+x)(2+x)/(3+x)]/(1x)/(3+x)=0,2336[x(3+x)×(2+x)(3+x)]÷(1x)(3+x)=0.2336It should be noted straight off that 3+x0sox3[x(3+x)×(2+x)(3+x)]×(3+x)(1x)=0.2336the (x+3) cancels,and x1[x(3+x)×(2+x)1]×1(1x)=0.2336x(2+x)(3+x)(1x)=0.2336x(2+x)(3+x)(1x)=0.2336Now multiply everything by the lowest common denominator (3+x)(1-x) to get rid of the fractionx(2+x)=0.2336(3+x)(1x)

 

you can keep going from here and solve it with the quadratic formula or you can just plug your initial equation into the site calc and get it to do it all for you.  

(x/(3+x) * (2+x)/(3+x) ) / (1-x)/(3+x) = 0.2336  

change the square brackets to round ones and change your decimal comma to a decimal point and just plug it in.

 

{\frac{{\frac{\left({\frac{{\frac{{\mathtt{x}}}{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}}{\mathtt{\,\times\,}}\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}}\right)}{\left({\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{x}}\right)}}}{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}} = {\mathtt{0.233\: \!6}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{\,-\,}}{\frac{{\mathtt{14\,508}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}}{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{704\,375}}}{\left({\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{502}}}{{\mathtt{219}}}}}}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}{\left({\mathtt{876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}\right)}}{\mathtt{\,-\,}}{\mathtt{2}}\\ {\mathtt{x}} = {\frac{{\sqrt{{\mathtt{\,-\,}}{\frac{{\mathtt{14\,508}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}}{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{704\,375}}}{\left({\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{502}}}{{\mathtt{219}}}}}}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}{\left({\mathtt{876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}\right)}}{\mathtt{\,-\,}}{\mathtt{2}}\\ {\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\sqrt{{\frac{{\mathtt{14\,508}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}}{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{704\,375}}}{\left({\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{502}}}{{\mathtt{219}}}}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}{\left({\mathtt{876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}\right)}}{\mathtt{\,-\,}}{\mathtt{2}}\\ {\mathtt{x}} = {\frac{{\sqrt{{\frac{{\mathtt{14\,508}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}}{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{704\,375}}}{\left({\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{502}}}{{\mathtt{219}}}}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}{\left({\mathtt{876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}\right)}}{\mathtt{\,-\,}}{\mathtt{2}}\\ \end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{3.318\: \!755\: \!885\: \!933\: \!879\: \!7}}{\mathtt{\,-\,}}{\mathtt{2.004\: \!784\: \!814\: \!651\: \!891\: \!5}}{i}\\ {\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{3.318\: \!755\: \!885\: \!933\: \!879\: \!7}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.004\: \!784\: \!814\: \!651\: \!891\: \!5}}{i}\\ {\mathtt{x}} = -{\mathtt{2.184\: \!609\: \!027\: \!146\: \!14}}\\ {\mathtt{x}} = {\mathtt{0.822\: \!120\: \!799\: \!013\: \!899\: \!5}}\\ \end{array} \right\}

My goodness that looks horrible!

Let's see what the graph looks like and get the answer/s from there.

 

Alright there are your 2 answers.  I might keep going with the quadratic formula and get them that way.

x(2+x)=0.2336(3+x)(1x)x2+2x=0.2336(33x+xx2)x2+2x=0.2336(x22x+3)

I could just finish this by hand but I'mm goint to let the web 2 calc do it for me.

x2+2×x=0.2336×(x22×x+3){x=(103571+257)257x=(103571257)257}{x=2.2522353553601686x=0.2522353553601686}

There you go, that is better!

These 2 answers would have been included in the original calculator ouput but some other imaginary roots were included as well.  You probably do not need to worry about those. 

 Aug 10, 2014
 #1
avatar+118702 
+10
Best Answer

[ x/(3+x) * (2+x)/(3+x) ] / (1-x)/(3+x) = 0,2336

[x/(3+x)(2+x)/(3+x)]/(1x)/(3+x)=0,2336[x(3+x)×(2+x)(3+x)]÷(1x)(3+x)=0.2336It should be noted straight off that 3+x0sox3[x(3+x)×(2+x)(3+x)]×(3+x)(1x)=0.2336the (x+3) cancels,and x1[x(3+x)×(2+x)1]×1(1x)=0.2336x(2+x)(3+x)(1x)=0.2336x(2+x)(3+x)(1x)=0.2336Now multiply everything by the lowest common denominator (3+x)(1-x) to get rid of the fractionx(2+x)=0.2336(3+x)(1x)

 

you can keep going from here and solve it with the quadratic formula or you can just plug your initial equation into the site calc and get it to do it all for you.  

(x/(3+x) * (2+x)/(3+x) ) / (1-x)/(3+x) = 0.2336  

change the square brackets to round ones and change your decimal comma to a decimal point and just plug it in.

 

{\frac{{\frac{\left({\frac{{\frac{{\mathtt{x}}}{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}}{\mathtt{\,\times\,}}\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}}\right)}{\left({\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{x}}\right)}}}{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}} = {\mathtt{0.233\: \!6}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{\,-\,}}{\frac{{\mathtt{14\,508}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}}{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{704\,375}}}{\left({\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{502}}}{{\mathtt{219}}}}}}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}{\left({\mathtt{876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}\right)}}{\mathtt{\,-\,}}{\mathtt{2}}\\ {\mathtt{x}} = {\frac{{\sqrt{{\mathtt{\,-\,}}{\frac{{\mathtt{14\,508}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}}{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{704\,375}}}{\left({\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{502}}}{{\mathtt{219}}}}}}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}{\left({\mathtt{876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}\right)}}{\mathtt{\,-\,}}{\mathtt{2}}\\ {\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\sqrt{{\frac{{\mathtt{14\,508}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}}{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{704\,375}}}{\left({\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{502}}}{{\mathtt{219}}}}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}{\left({\mathtt{876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}\right)}}{\mathtt{\,-\,}}{\mathtt{2}}\\ {\mathtt{x}} = {\frac{{\sqrt{{\frac{{\mathtt{14\,508}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}}{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{704\,375}}}{\left({\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{502}}}{{\mathtt{219}}}}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\sqrt{{\mathtt{191\,844}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{219\,876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)}{\mathtt{\,-\,}}{\mathtt{704\,375}}}}}{\left({\mathtt{876}}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{625}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6\,484\,410\,131}}}}}{\left({\mathtt{219}}{\mathtt{\,\times\,}}{{\mathtt{146}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)}\right)}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{10\,930\,245\,625}}}{{\mathtt{84\,027\,672}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}\right)}}{\mathtt{\,-\,}}{\mathtt{2}}\\ \end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{3.318\: \!755\: \!885\: \!933\: \!879\: \!7}}{\mathtt{\,-\,}}{\mathtt{2.004\: \!784\: \!814\: \!651\: \!891\: \!5}}{i}\\ {\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{3.318\: \!755\: \!885\: \!933\: \!879\: \!7}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.004\: \!784\: \!814\: \!651\: \!891\: \!5}}{i}\\ {\mathtt{x}} = -{\mathtt{2.184\: \!609\: \!027\: \!146\: \!14}}\\ {\mathtt{x}} = {\mathtt{0.822\: \!120\: \!799\: \!013\: \!899\: \!5}}\\ \end{array} \right\}

My goodness that looks horrible!

Let's see what the graph looks like and get the answer/s from there.

 

Alright there are your 2 answers.  I might keep going with the quadratic formula and get them that way.

x(2+x)=0.2336(3+x)(1x)x2+2x=0.2336(33x+xx2)x2+2x=0.2336(x22x+3)

I could just finish this by hand but I'mm goint to let the web 2 calc do it for me.

x2+2×x=0.2336×(x22×x+3){x=(103571+257)257x=(103571257)257}{x=2.2522353553601686x=0.2522353553601686}

There you go, that is better!

These 2 answers would have been included in the original calculator ouput but some other imaginary roots were included as well.  You probably do not need to worry about those. 

Melody Aug 10, 2014
 #2
avatar+130477 
+5

WolframAlpha gets a slightly different result from Melody's answer...I suspect the reason is in the way that WA is interpreting the multiple divisions of the two functions outside the brackets....

(The only change I made to the original problem was to subtract .2336 from both sides....)

 

Whatever.....I think the point here is that this one would be a tough one to evaluate by hand.......Based on the original form of the problem, it would be difficult to intuit how many "real' and/or "non-real" solutions there might be......

 

 Aug 10, 2014
 #3
avatar
0

thank you both ! 

 Aug 10, 2014

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