Solving a literal equation containing fractions. I know this might seem very simple, but I can't seem to isolate x.
$$\frac{1}{x} = \frac{1}{a} + \frac{1}{b} $$
Please show me the steps to solving it.

$\frac{1}{x} = \frac{b}{ab} + \frac{a}{ab}$
$\frac{1}{x} = \frac{a + b}{ab}$
$x = \frac{ab}{a + b}$
note that $\frac{1}{x} = \frac{1}{a} + \frac{1}{b}$ is possible if and only if $\frac{1}{a} + \frac{1}{b} \neq 0$. This implies that $a \neq -b$; and, hence $a + b \neq 0$. 
