# Math Help - Simplifying Rationals

1. ## Simplifying Rationals

http://img14.imageshack.us/img14/5564/11102137.jpg

i had to save the picture and upload it because the equations wouldnt come out right in the text box. just zoom in the picture and itss fine.

2. Originally Posted by Auger
http://img14.imageshack.us/img14/5564/11102137.jpg

i had to save the picture and upload it because the equations wouldnt come out right in the text box. just zoom in the picture and itss fine.
Hi Auger,

Here's the first one.

$\frac{1}{x^2-x-2}-\frac{x}{x^2-5x+6}$

$\frac{1}{(x-2)(x+1)}-\frac{x}{(x-3)(x-2)}$

$\frac{1(x-3)-x(x+1)}{(x+1)(x-2)(x-3)}$

$\frac{x-3-x^2-x}{(x+1)(x-2)(x-3)}$

$\frac{-(x^2+3)}{(x+1)(x-2)(x-3)}$

3. And the second one...Seems like there aught to be an easier way, but here goes. Maybe an algebraist will step in and clean it up.

$\frac{-x}{(x+1)^{\frac{3}{2}}}+\frac{2}{(x+1)^{\frac{1}{2 }}}$

$\frac{-x}{(\sqrt{x+1})^3}+\frac{2}{\sqrt{x+1}}$

$\frac{-x+2(\sqrt{x+1})^2}{(\sqrt{x+1})^3}$

$\frac{-x+2(x+1)}{(\sqrt{x+1})^3}$

$\frac{x+2}{(\sqrt{x+1})^3} \cdot \frac{\sqrt{x+1}}{\sqrt{x+1}}$

$\frac{(x+2)(\sqrt{x+1})}{(x+1)^2}$

$\frac{(x+2)(x+1)^{\frac{1}{2}}}{(x+1)^2}$

$\boxed{\frac{x+2}{(x+1)^{\frac{3}{2}}}}$

4. thanks so much man. the reason i wasnt getting the right answers was because i wasnt simplifying enough in the first steps, which caused me to continue getting the wrong answer. + rep and thanks fo sho hahaha