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## anonymous 4 years ago simplify completely (x^2-100/x^2+2x-120)/(6 x+60/x-2)

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1. anonymous

i'll give you a medal if you hurry up! :3

2. ash2326

We have $\frac{x^2-100}{x^2+2x-120}/\frac{6 x+60}{x-2}$ it can also be written as $\frac{x^2-100}{x^2+2x-120}*\frac{x-2}{6 x+60}$ now a^2-b^2= (a+b)(a-b) so, (x^2-100)=(x+10)(x-10) let's find the factors of (x^2+2x-120)=(x+12)(x-10) so the express ion can be rewritten as $\frac{(x-10)(x+10)}{(x+12)(x-10)}*\frac{x-2}{6 x+60}$ 6x+60=6(x+10) $\frac{(x-10)(x+10)}{(x+12)(x-10)}*\frac{x-2}{6 (x+10)}$ let's cancel the common factors $\frac{\cancel{(x-10)}\cancel{(x+10)}}{(x+12)\cancel{(x-10)}}*\frac{x-2}{6 \cancel{(x+10)}}$ so we get finally $\frac{(x-2)}{6(x+12)}$

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