# Math Help - Rational Expression Help

1. ## Rational Expression Help

Hi,

I am currently studying for the GMAT and came across the following problem that I seem to be having trouble understanding.

Multiply 4X/X2 -16 x X+4/2X2

The book I am using provides the answer but no context for getting it. Any help is much appreciated.

2. ## Re: Rational Expression Help

Hello, benlh1!

$\text{Simplify: }\:\frac{4x}{x^2-16} \times \frac{x+4}{2x^2}$

We have: . $\frac{4x(x+4)}{2x^2(x^2-16)}$

Factor: . $\frac{2\cdot2\cdot x\cdot(x+4)}{2\cdot x \cdot x(x-4)(x+4)}$

Reduce: . $\frac{{\color{red}\rlap{/}}2\cdot2\cdot{\color{red}\rlap{/}}x\cdot({\color{red}\rlap{/////}}x+4)}{{\color{red}\rlap{/}}2\cdot{\color{red}\rlap{/}}x \cdot x(x-4)({\color{red}\rlap{/////}}x+4)}$

Answer: . $\frac{2}{x(x-4)}$