Answer
$\dfrac{ab}{b-a}$
Work Step by Step
Using $a^{-1}=\dfrac{1}{a}$, the expression $
\left( a^{-1}-b^{-1} \right)^{-1}
$ simplifies to
\begin{array}{l}
\left( \dfrac{1}{a}-\dfrac{1}{b} \right)^{-1}
\\\\=
\left( \dfrac{b-a}{ab} \right)^{-1}
\\\\=
\dfrac{ab}{b-a}
.\end{array}
