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