# How do you simplify (a^-1 + b^-1)^-1?

Jan 10, 2016

$\frac{a b}{a + b}$
Write ${a}^{-} 1$ as $\frac{1}{a}$ and ${b}^{-} 1$ as $\frac{1}{b}$
${\left(\frac{1}{a} + \frac{1}{b}\right)}^{-} 1 = {\left(\frac{a + b}{a b}\right)}^{-} 1 = \frac{a b}{a + b}$