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The fraction:


should simplify to the answer:


but the best I could do was expand it to:


What's next step?

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up vote 4 down vote accepted

For $x \neq y$, $$\frac{(y+x)(y-x)}{x-y} = \frac{(y+x)(y-x)}{-(y-x)}$$

$$ = -(y+x)$$ $$ = -(x+y)$$

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only if $x \neq y$ – I. J. Kennedy Feb 4 '11 at 0:55
I.J. Kennedy: Well, the original expression wouldn't have made sense if $x=y$. – Fredrik Meyer Feb 6 '11 at 15:02

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