$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}6x^{4}-6x^{3}+6x^{2}-6x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}6x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-6x^{5}-6x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{5}-6x^{4};}-6x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}6x^{4}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{4}+6x^{3}-;x^n;}\phantom{;}6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-6x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-6x^{3}-6x^{2}-;x^n-;x^n;}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}6x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}6x^{2}+6x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}6x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{-6x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;;;;-6x\phantom{;}-6\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-6\phantom{;}\phantom{;}\\\end{array}$

$6x^{4}-6x^{3}+6x^{2}-6x+6+\frac{-6}{1+x}$