$\begin{array}{l}\phantom{\phantom{;}2y\phantom{;}+3;}{\phantom{;}16y^{4}-24y^{3}+36y^{2}-54y\phantom{;}+81\phantom{;}\phantom{;}}\\\phantom{;}2y\phantom{;}+3\overline{\smash{)}\phantom{;}32y^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-243\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2y\phantom{;}+3;}\underline{-32y^{5}-48y^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-32y^{5}-48y^{4};}-48y^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-243\phantom{;}\phantom{;}\\\phantom{\phantom{;}2y\phantom{;}+3-;x^n;}\underline{\phantom{;}48y^{4}+72y^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}48y^{4}+72y^{3}-;x^n;}\phantom{;}72y^{3}\phantom{-;x^n}\phantom{-;x^n}-243\phantom{;}\phantom{;}\\\phantom{\phantom{;}2y\phantom{;}+3-;x^n-;x^n;}\underline{-72y^{3}-108y^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-72y^{3}-108y^{2}-;x^n-;x^n;}-108y^{2}\phantom{-;x^n}-243\phantom{;}\phantom{;}\\\phantom{\phantom{;}2y\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}108y^{2}+162y\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}108y^{2}+162y\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}162y\phantom{;}-243\phantom{;}\phantom{;}\\\phantom{\phantom{;}2y\phantom{;}+3-;x^n-;x^n-;x^n-;x^n;}\underline{-162y\phantom{;}-243\phantom{;}\phantom{;}}\\\phantom{;;;;-162y\phantom{;}-243\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-486\phantom{;}\phantom{;}\\\end{array}$

$16y^{4}-24y^{3}+36y^{2}-54y+81+\frac{-486}{2y+3}$