$\begin{array}{l}\phantom{\phantom{;}5y\phantom{;}+4;}{\phantom{;}4y^{2}-5y\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}5y\phantom{;}+4\overline{\smash{)}\phantom{;}20y^{3}-9y^{2}\phantom{-;x^n}+18\phantom{;}\phantom{;}}\\\phantom{\phantom{;}5y\phantom{;}+4;}\underline{-20y^{3}-16y^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-20y^{3}-16y^{2};}-25y^{2}\phantom{-;x^n}+18\phantom{;}\phantom{;}\\\phantom{\phantom{;}5y\phantom{;}+4-;x^n;}\underline{\phantom{;}25y^{2}+20y\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}25y^{2}+20y\phantom{;}-;x^n;}\phantom{;}20y\phantom{;}+18\phantom{;}\phantom{;}\\\phantom{\phantom{;}5y\phantom{;}+4-;x^n-;x^n;}\underline{-20y\phantom{;}-16\phantom{;}\phantom{;}}\\\phantom{;;-20y\phantom{;}-16\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}2\phantom{;}\phantom{;}\\\end{array}$

$4y^{2}-5y+4+\frac{2}{5y+4}$