Answer
$\displaystyle \frac{2(x^{2}-2)}{x(x+2)(x-2)}$
Work Step by Step
Factor the first denominator
$x^{2}-4 =x^{2}-2^{2}=(x+2)(x-2).$
LCD = $x(x+2)(x-2)$
$\displaystyle \frac{x}{x^{2}-4}+\frac{1}{x}=\frac{x}{(x+2)(x-2)}+\frac{1}{x}$
$=\displaystyle \frac{x\cdot x+1\cdot(x+2)(x-2)}{x(x+2)(x-2)}$
$=\displaystyle \frac{x^{2}+(x^{2}-4)}{x(x+2)(x-2)}$
$=\displaystyle \frac{2x^{2}-4}{x(x+2)(x-2)}$
$=\displaystyle \frac{2(x^{2}-2)}{x(x+2)(x-2)}$
