Answer
$\dfrac{x^2+xy}{y^3+y^2}$
Work Step by Step
The expression $
\dfrac{\dfrac{x}{y^2}+\dfrac{1}{y}}{\dfrac{y}{x^2}+\dfrac{1}{x}}
$ simplifies to
\begin{array}{l}
\left( \dfrac{x}{y^2}+\dfrac{1}{y}\right) \div\left( \dfrac{y}{x^2}+\dfrac{1}{x} \right)
\\\\=
\dfrac{x+y}{y^2} \div\dfrac{xy+x}{x^2}
\\\\=
\dfrac{x+y}{y^2} \cdot\dfrac{x^2}{xy+x}
\\\\=
\dfrac{x+y}{y^2} \cdot\dfrac{x\cdot x}{x(y+1)}
\\\\=
\dfrac{x+y}{y^2} \cdot\dfrac{x}{y+1}
\\\\=
\dfrac{x^2+xy}{y^3+y^2}
.\end{array}
