Answer
$\frac{ 2(x^2-2)}{x(x-2)(x+2)}$
Work Step by Step
Since the least common multiple (LCM) of the denominator is $x(x-2)(x+2)$, then we have
$$
\frac{x}{x^2-4}+\frac{1}{x}=\frac{x^2}{x(x-2)(x+2)}+\frac{(x-2)(x+2)}{x(x-2)(x+2)}
.$$
Now, since the denominators are the same, then we have
$$
\frac{x^2}{x(x-2)(x+2)}+\frac{(x-2)(x+2)}{x(x-2)(x+2)}=\frac{x^2+x^2-4}{x(x-2)(x+2)}\\
=\frac{ 2(x^2-2)}{x(x-2)(x+2)}
.$$
