+0  
 
+1
61
2
avatar+175 

 what is the simplified form of the complex fraction?

 

jbouyer  Nov 21, 2017

Best Answer 

 #2
avatar+1493 
+3

1) 

 

\(\frac{\textcolor{red}{\frac{3}{x}+\frac{1}{4}}}{\textcolor{blue}{1+\frac{3}{x}}}\) is quite the complex fraction. First, let's just deal with the numerator

 

\(\textcolor{red}{\frac{3}{x}+\frac{1}{4}}\)First. let's change this into fractions with common denominators. The LCM is 4x.
\(\frac{12}{4x}+\frac{x}{4x}\)Now, combine the fractions because we have formed a common denominator.
\(\frac{12+x}{4x}\) 
  

 

\(\textcolor{blue}{1+\frac{3}{x}}\)Just like before, transform the fractions to create a common denominator and combine.
\(\frac{x}{x}+\frac{3}{x}\) 
\(\frac{x+3}{x}\) 
  

 

Now, write it as a fraction; you'll see how much easier it is to work with!
 

\(\frac{\textcolor{red}{\frac{3}{x}+\frac{1}{4}}}{\textcolor{blue}{1+\frac{3}{x}}}=\frac{\frac{12+x}{4x}}{\frac{x+3}{x}}\) 
\(\frac{\frac{12+x}{4x}}{\frac{x+3}{x}}\)Multiply by \(\frac{x}{x+3}\), the reciprocal of the complex denominator, to eliminate this complex fraction.
\(\frac{x(12+x)}{4x(x+3)}\)The x in the numerator and the x in the denominator cancel out here.
\(\frac{12+x}{4(x+3)}\)Now, distribute the 4 into every term.
\(\frac{12+x}{4x+12}\) 
  

 

 

2) \(\frac{c^2-4c+4}{12c^3+30c^2}\div\frac{c^2-4}{6c^4+15c^3}\)

 

Dividing by a fraction is the same as multiplying by its reciprocal.

 

\(\frac{c^2-4c+4}{12c^3+30c^2}*\frac{6c^4+15c^3}{c^2-4}\)

 

Now, let's factor the numerators and denominators completely and fully and see if any canceling can occur to simplify this.

 

\(\frac{c^2-4c+4}{12c^3+30c^2}*\frac{6c^4+15c^3}{c^2-4}\)Factor everything fully.
\(\frac{(c-2)^2}{6c^2(2c+5)}*\frac{3c^3(2c+5)}{(c+2)(c-2)}\)I see a lot of canceling that will occur here, dont you?
\(\frac{c-2}{2}*\frac{c}{c+2}\)Now, combine.
\(\frac{c(c-2)}{2(c+2)}\)This answer corresponds to the third one listed in the multiple guess.
  
TheXSquaredFactor  Nov 22, 2017
edited by TheXSquaredFactor  Nov 22, 2017
Sort: 

2+0 Answers

 #1
avatar
+1

X^2 answer is much simpler and easier to follow.

Guest Nov 22, 2017
edited by Guest  Nov 22, 2017
 #2
avatar+1493 
+3
Best Answer

1) 

 

\(\frac{\textcolor{red}{\frac{3}{x}+\frac{1}{4}}}{\textcolor{blue}{1+\frac{3}{x}}}\) is quite the complex fraction. First, let's just deal with the numerator

 

\(\textcolor{red}{\frac{3}{x}+\frac{1}{4}}\)First. let's change this into fractions with common denominators. The LCM is 4x.
\(\frac{12}{4x}+\frac{x}{4x}\)Now, combine the fractions because we have formed a common denominator.
\(\frac{12+x}{4x}\) 
  

 

\(\textcolor{blue}{1+\frac{3}{x}}\)Just like before, transform the fractions to create a common denominator and combine.
\(\frac{x}{x}+\frac{3}{x}\) 
\(\frac{x+3}{x}\) 
  

 

Now, write it as a fraction; you'll see how much easier it is to work with!
 

\(\frac{\textcolor{red}{\frac{3}{x}+\frac{1}{4}}}{\textcolor{blue}{1+\frac{3}{x}}}=\frac{\frac{12+x}{4x}}{\frac{x+3}{x}}\) 
\(\frac{\frac{12+x}{4x}}{\frac{x+3}{x}}\)Multiply by \(\frac{x}{x+3}\), the reciprocal of the complex denominator, to eliminate this complex fraction.
\(\frac{x(12+x)}{4x(x+3)}\)The x in the numerator and the x in the denominator cancel out here.
\(\frac{12+x}{4(x+3)}\)Now, distribute the 4 into every term.
\(\frac{12+x}{4x+12}\) 
  

 

 

2) \(\frac{c^2-4c+4}{12c^3+30c^2}\div\frac{c^2-4}{6c^4+15c^3}\)

 

Dividing by a fraction is the same as multiplying by its reciprocal.

 

\(\frac{c^2-4c+4}{12c^3+30c^2}*\frac{6c^4+15c^3}{c^2-4}\)

 

Now, let's factor the numerators and denominators completely and fully and see if any canceling can occur to simplify this.

 

\(\frac{c^2-4c+4}{12c^3+30c^2}*\frac{6c^4+15c^3}{c^2-4}\)Factor everything fully.
\(\frac{(c-2)^2}{6c^2(2c+5)}*\frac{3c^3(2c+5)}{(c+2)(c-2)}\)I see a lot of canceling that will occur here, dont you?
\(\frac{c-2}{2}*\frac{c}{c+2}\)Now, combine.
\(\frac{c(c-2)}{2(c+2)}\)This answer corresponds to the third one listed in the multiple guess.
  
TheXSquaredFactor  Nov 22, 2017
edited by TheXSquaredFactor  Nov 22, 2017

20 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details