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I know that the answer is $-(3 + h)$, but I'm not sure how to get there.

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up vote 8 down vote accepted

Notice that $(h-3)=-(3-h)$. Do you see what to do now?

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So, I can now cancel that with the (3 - h) and am left with (3 + h)/-1, which is -( 3 + h ). Thank you! – Jason T Featheringham Sep 16 '12 at 19:39

Since your fraction is $\dfrac {(3-h)(3+h)}{h - 3}$ and the two terms $3-h$ in the numerator and $h-3$ in the denominator are only different in a minus sign, they'll be cancelled out and the term in numerator remains which is $3+h$ multiplying by a minus sign.

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