Chapter A.5, Problem 27AYU

To determine

To find: Simplify the given in factored form.

Answer to Problem 27AYU

$\frac{2\left(2x^2+5x-2\right)}{\left(x+3\right)\left(x+2\right)\left(x-2\right)}$

Explanation of Solution

Given:

$\frac{4x}{x^2-4}-\frac{2}{x^2+x-6}$

Calculation:

$\frac{4x}{x^2-4}-\frac{2}{x^2+x-6}=\frac{4x}{\left(x+2\right)\left(x-2\right)}-\frac{2}{\left(x+3\right)\left(x-2\right)}=\frac{2\left(2x^2+5x-2\right)}{\left(x+3\right)\left(x+2\right)\left(x-2\right)}$