Answer
$\dfrac{2a}{a-1}$
Work Step by Step
The expression $
\dfrac{\dfrac{a}{5}}{\dfrac{a-1}{10}}
$ simplifies to
\begin{array}{l}
\dfrac{a}{5}\div\dfrac{a-1}{10}
\\\\=
\dfrac{a}{5}\cdot\dfrac{10}{a-1}
\\\\=
\dfrac{a}{5}\cdot\dfrac{5\cdot2}{a-1}
\\\\=
\dfrac{2a}{a-1}
.\end{array}
