Question

simplify completely (x^2-100/x^2+2x-120)/(6 x+60/x-2)

Answer 1

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

Answer 2

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
\[\frac{(x-2)}{6(x+12)}\]