$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+6;}{-x^{5}+6x^{4}-36x^{3}+216x^{2}-1296x\phantom{;}+7776\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+6\overline{\smash{)}-x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1296\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+6;}\underline{\phantom{;}x^{6}+6x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{6}+6x^{5};}\phantom{;}6x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1296\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n;}\underline{-6x^{5}-36x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-6x^{5}-36x^{4}-;x^n;}-36x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1296\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n;}\underline{\phantom{;}36x^{4}+216x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}36x^{4}+216x^{3}-;x^n-;x^n;}\phantom{;}216x^{3}\phantom{-;x^n}\phantom{-;x^n}+1296\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n-;x^n;}\underline{-216x^{3}-1296x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-216x^{3}-1296x^{2}-;x^n-;x^n-;x^n;}-1296x^{2}\phantom{-;x^n}+1296\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}1296x^{2}+7776x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;\phantom{;}1296x^{2}+7776x\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}7776x\phantom{;}+1296\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-7776x\phantom{;}-46656\phantom{;}\phantom{;}}\\\phantom{;;;;;-7776x\phantom{;}-46656\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}-45360\phantom{;}\phantom{;}\\\end{array}$

$-x^{5}+6x^{4}-36x^{3}+216x^{2}-1296x+7776+\frac{-45360}{x+6}$