$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+6;}{\phantom{;}x^{4}-6x^{3}+36x^{2}-216x\phantom{;}+1296\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+6\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+243\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+6;}\underline{-x^{5}-6x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-6x^{4};}-6x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+243\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n;}\underline{\phantom{;}6x^{4}+36x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{4}+36x^{3}-;x^n;}\phantom{;}36x^{3}\phantom{-;x^n}\phantom{-;x^n}+243\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n;}\underline{-36x^{3}-216x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-36x^{3}-216x^{2}-;x^n-;x^n;}-216x^{2}\phantom{-;x^n}+243\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n-;x^n;}\underline{\phantom{;}216x^{2}+1296x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}216x^{2}+1296x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}1296x\phantom{;}+243\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n-;x^n-;x^n;}\underline{-1296x\phantom{;}-7776\phantom{;}\phantom{;}}\\\phantom{;;;;-1296x\phantom{;}-7776\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-7533\phantom{;}\phantom{;}\\\end{array}$

$x^{4}-6x^{3}+36x^{2}-216x+1296+\frac{-7533}{x+6}$