Answer
$\dfrac{xy+2x^3}{y-1}$
Work Step by Step
The factored form of the given expression, $
\dfrac{x^{-1}+2xy^{-1}}{x^{-2}-x^{-2}y^{-1}}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{1}{x}+\dfrac{2x}{y}}{\dfrac{1}{x^2}-\dfrac{1}{x^2y^1}}
\\\\=
\dfrac{\dfrac{y+2x^2}{xy}}{\dfrac{y-1}{x^2y}}
\\\\=
\dfrac{y+2x^2}{xy}\div\dfrac{y-1}{x^2y}
\\\\=
\dfrac{y+2x^2}{xy}\cdot\dfrac{x^2y}{y-1}
\\\\=
\dfrac{y+2x^2}{\cancel{xy}}\cdot\dfrac{\cancel{xy}\cdot x}{y-1}
\\\\=
\dfrac{xy+2x^3}{y-1}
.\end{array}
