$\begin{array}{l}\phantom{\phantom{;}y^{4}-y^{2};}{\phantom{;}4y\phantom{;}\phantom{-;x^n}}\\\phantom{;}y^{4}-y^{2}\overline{\smash{)}\phantom{;}4y^{5}\phantom{-;x^n}+5y^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}y^{4}-y^{2};}\underline{-4y^{5}\phantom{-;x^n}+4y^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4y^{5}+4y^{3};}\phantom{;}9y^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\end{array}$

$4y+\frac{9y^{3}}{y^4-y^2}$