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Math Help - simpify expression

  1. #1
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    simpify expression

    Hey guys, need help simplifing this expression..
    <br /> <br />
\frac{x}{y-x} - \frac{y}{y+x} - \frac{2xy}{y^2-x^2}<br /> <br />


    thank u
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  2. #2
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    Quote Originally Posted by jvignacio View Post
    Hey guys, need help simplifing this expression..
    <br /> <br />
\frac{x}{y-x} - \frac{y}{y+x} - \frac{2xy}{y^2-x^2}<br /> <br />


    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

    <br /> <br />
\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)}<br /> <br />

    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
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