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