Answer
$\dfrac{5y-3x^2}{x(y+x)}$
Work Step by Step
The given expression, $
\dfrac{5x^{-2}-3y^{-1}}{x^{-1}+y^{-1}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{5}{x^2}-\dfrac{3}{y}}{\dfrac{1}{x}+\dfrac{1}{y}}
\\\\=
\dfrac{\dfrac{5y-3x^2}{x^2y}}{\dfrac{y+x}{xy}}
\\\\=
\dfrac{5y-3x^2}{x^2y}\div\dfrac{y+x}{xy}
\\\\=
\dfrac{5y-3x^2}{x^2y}\cdot\dfrac{xy}{y+x}
\\\\=
\dfrac{5y-3x^2}{\cancel{xy}\cdot x}\cdot\dfrac{\cancel{xy}}{y+x}
\\\\=
\dfrac{5y-3x^2}{x(y+x)}
.\end{array}
