# simplifying expression help.

• Nov 3rd 2008, 10:57 AM
Tweety
simplifying expression help.
$\displaystyle \frac{x + y - (x^2 + y^2)}{x + y }$

dont know were to start
• Nov 3rd 2008, 12:22 PM
masters
Quote:

Originally Posted by Tweety
$\displaystyle \frac{x + y - (x^2 + y^2)}{x + y }$

dont know were to start

You might change it to this, but I'm not sure if that's a simplification.

$\displaystyle \frac{x+y}{x+y}-\frac{x^2+y^2}{x+y}=1-\frac{x^2+y^2}{x+y}$
• Nov 3rd 2008, 12:25 PM
Tweety
Quote:

Originally Posted by masters
You might change it to this, but I'm not sure if that's a simplification.

$\displaystyle \frac{x+y}{x+y}-\frac{x^2+y^2}{x+y}=1-\frac{x^2+y^2}{x+y}$

Hi,

thanks for replying but apparently the answer is $\displaystyle \frac{2xy}{x +y}$ I don't know how to get to this.
• Nov 8th 2008, 08:20 AM
Chop Suey
Use polynomial long division.
• Nov 8th 2008, 08:23 AM
Moo
Hello,

Complete a square :
$\displaystyle x^2+y^2=x^2+y^2+2xy-2xy=(x+y)^2-2xy$

So we have :

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

(Tongueout)