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

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