$\begin{array}{l}\phantom{\phantom{;}h\phantom{;}-3;}{\phantom{;}h^{3}+6h^{2}+18h\phantom{;}+55\phantom{;}\phantom{;}}\\\phantom{;}h\phantom{;}-3\overline{\smash{)}\phantom{;}h^{4}+3h^{3}\phantom{-;x^n}+h\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}h\phantom{;}-3;}\underline{-h^{4}+3h^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-h^{4}+3h^{3};}\phantom{;}6h^{3}\phantom{-;x^n}+h\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}h\phantom{;}-3-;x^n;}\underline{-6h^{3}+18h^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-6h^{3}+18h^{2}-;x^n;}\phantom{;}18h^{2}+h\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}h\phantom{;}-3-;x^n-;x^n;}\underline{-18h^{2}+54h\phantom{;}\phantom{-;x^n}}\\\phantom{;;-18h^{2}+54h\phantom{;}-;x^n-;x^n;}\phantom{;}55h\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}h\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-55h\phantom{;}+165\phantom{;}\phantom{;}}\\\phantom{;;;-55h\phantom{;}+165\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}160\phantom{;}\phantom{;}\\\end{array}$

$h^{3}+6h^{2}+18h+55+\frac{160}{h-3}$