+0  
 
0
422
3
avatar+555 

How would I express (2x - 1) / (x + 2) as A + B / (x+2), where A and B are integers?

I can do 2x / (x + 2) - 1 / (x+2) of course, but that doesn't work...

Any ideas?

 

EDIT: Sorry if I wasn't clear, but it's NOT:

 $${\frac{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}} = {\mathtt{A}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{B}}}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}$$

But instead I need to change:

$${\frac{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}$$

Into something that looks like:

$${\mathtt{A}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{B}}}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}$$

Thank you!

Will85237  Jan 19, 2015

Best Answer 

 #2
avatar+92624 
+10

I think anon's logic should work but I would do it much more simply.

 

$$\frac{2x-1 }{ x+2}\\\\
=\frac{2(x+2)-1-4}{x+2}\\\\
=\frac{2(x+2)-5}{x+2}\\\\
=\frac{2(x+2)}{x+2}+\frac{-5}{x+2}\\\\
=2+\frac{-5}{x+2}$$

 

Don't give anon negative points for trying to help you!!!

Melody  Jan 19, 2015
 #1
avatar
+5

Start by multiplying both sides by (x+2), giving 2x-1 = A(x+2)+B

Now, multiply out and equate x terms on the left to x terms on the right, and we have A=2, and also -1=2A+B

Now just solve for B. 🚲

Guest Jan 19, 2015
 #2
avatar+92624 
+10
Best Answer

I think anon's logic should work but I would do it much more simply.

 

$$\frac{2x-1 }{ x+2}\\\\
=\frac{2(x+2)-1-4}{x+2}\\\\
=\frac{2(x+2)-5}{x+2}\\\\
=\frac{2(x+2)}{x+2}+\frac{-5}{x+2}\\\\
=2+\frac{-5}{x+2}$$

 

Don't give anon negative points for trying to help you!!!

Melody  Jan 19, 2015
 #3
avatar+92624 
+5

YES anon understood what you wanted and gave you a correct answer!

I shall show you

 

$$\\\frac{2x-1}{x+2}=A+\frac{B}{x+2}\\\\
$multiply both sides by (x+2)$\\
2x-1=A(x+2)+B\\
2x-1=Ax+2A+B\\
2x-1=Ax+(2A+B)\\
$ equating co-efficients$\\
2=A\\
-1=2A+B\\
-1=4+B\\
B=-5\\
so\\
\frac{2x-1}{x+2}=2+\frac{-5}{x+2}\\\\$$

 

so maybe you owe anon an appology  

Melody  Jan 19, 2015

6 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.