Answer
$\dfrac{2(x^2-2)}{x(x+2)(x-2)}$
Work Step by Step
The LCD is $x(x^2-4)$.
Make the expressions similar by multiplying $x$ to both the numerator and denominator of the first expression multiplying $x^2-4$ to both the numerator and denominator of the second expression to obtain:
$=\dfrac{x}{x^2-4}\cdot \dfrac{x}{x}+\dfrac{1}{x} \cdot\dfrac{x^2-4}{x^2-4}$
$=\dfrac{x^2}{x(x^2-4)}+\dfrac{x^2-4}{x(x^2-4)}$
Add the numerators and retain the denominator to obtain:
$=\dfrac{x^2+x^2-4}{x(x^2-4)}$
$=\dfrac{2x^2-4}{x(x^2-2^2)}$
Factor each polynomial completely.
Use special formula $a^2-b^2=(a+b)(a-b)$ to obtain:
$=\dfrac{2(x^2-2)}{x(x+2)(x-2)}$
