# Math Help - simplifying expression help.

1. ## simplifying expression help.

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

dont know were to start

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

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

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

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

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

Hi,

thanks for replying but apparently the answer is $\frac{2xy}{x +y}$ I don't know how to get to this.

4. Use polynomial long division.

5. Hello,

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

So we have :

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