Answer
$\dfrac{1+a}{1-a}$
Work Step by Step
The given expression, $
\dfrac{a^{-1}+1}{a^{-1}-1}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{1}{a^1}+1}{\dfrac{1}{a^1}-1}
\\\\=
\dfrac{\dfrac{1+a}{a}}{\dfrac{1-a}{a}}
\\\\=
\dfrac{\dfrac{1+a}{\cancel{a}}}{\dfrac{1-a}{\cancel{a}}}
\\\\=
\dfrac{1+a}{1-a}
.\end{array}
