# Thread: simpify expression

1. ## simpify expression

Hey guys, need help simplifing this expression..
$

\frac{x}{y-x} - \frac{y}{y+x} - \frac{2xy}{y^2-x^2}

$

thank u

2. Originally Posted by jvignacio
Hey guys, need help simplifing this expression..
$

\frac{x}{y-x} - \frac{y}{y+x} - \frac{2xy}{y^2-x^2}

$

thank u
First we need to find the LCD of all three fractions

Lets start with $y^2-x^2=(y-x)(y+x)$ This is the lowest common denominator

so now we build each fraction to have the same denomniantor

$

\frac{x}{y-x}\left( \frac{x+y}{x+y} \right) - \frac{y}{y+x}\left( \frac{y-x}{y-x} \right) - \frac{2xy}{(y-x)(y+x)}

$

Now lets multiply out the numerators and simplify

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

$\frac{(x-y)(x+y)}{(y-x)(y+x)}=-1 \mbox{ if } x \ne y$