# Simplify Equation

• Jan 30th 2010, 05:29 PM
sprivitor
Simplify Equation
I am unable to come up with the answer to the key for this problem. Can someone give it a try?

(4x^2+x-6)/(x^2+3x+2)-3x/(x+1)+5/(x+2)

• Jan 30th 2010, 05:49 PM
Sudharaka
Dear sprivitor,

$\displaystyle \frac{4x^2+x-6}{(x+1)(x+2)}-\frac{3x}{x+1}+\frac{5}{x+2}$

$\displaystyle \frac{4x^2+x-6-3x(x+2)+5(x+1)}{(x+1)(x+2)}$

By simplification we would get,

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

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

$\displaystyle \frac{x+1}{x+2}$

Hope this helps.
• Jan 30th 2010, 05:53 PM
Wilmer
[quote=sprivitor;448278]I am unable to come up with the answer to the key for this problem. Can someone give it a try?
(4x^2+x-6)/(x^2+3x+2)-3x/(x+1)+5/(x+2)
[quote]
Did you realise that x^2+3x+2 = (x+1)(x+2) ?
• Jan 30th 2010, 06:09 PM
sprivitor
Thank you. I now see my problem was with a simple negative sign.

-3X/(X+1) + 5 / (X+2)

I made the WRONG assumption that this equals

-[3X/(X+1) + 5 / (X+2)]

it is equal to

-[3X/(X+1) - 5 / (X+2)]