# Thread: Simplifying and multiplying a rational expression

1. ## Simplifying and multiplying a rational expression

This problem is really overwhelming to me. I've tried breaking it down, but I always end up screwing up somewhere. Can someone help me break it out down step by step?

Multiply and simplify: $\frac{{\frac{{{{x}}^{{2}}-{3}{x}-{10}}}{{{{x}}^{{2}}+{2}{x}-{8}}}}}{{\frac{{{x}+{2}}}{{{x}-{2}}}}}$

2. ## Re: Simplifying and multiplying a rational expression

Originally Posted by DasRabbit
Multiply and simplify: $\frac{{\frac{{{{x}}^{{2}}-{3}{x}-{10}}}{{{{x}}^{{2}}+{2}{x}-{8}}}}}{{\frac{{{x}+{2}}}{{{x}-{2}}}}}$
$=\frac{(x-2)\left(x^2-3x-10\right)}{(x+2)\left(x^2+2x-8\right)}$

3. ## Re: Simplifying and multiplying a rational expression

Originally Posted by MaxJasper
$=\frac{(x-2)\left(x^2-3x-10\right)}{(x+2)\left(x^2+2x-8\right)}$
Each of the quadratics also factorises, which should lead to some nice cancellation