$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}x^{4}+x^{3}-2x^{2}-2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}-6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-x^{5}+x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+x^{4};}\phantom{;}x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-x^{4}+x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-x^{4}+x^{3}-;x^n;}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{\phantom{;}2x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}2x^{3}-2x^{2}-;x^n-;x^n;}-2x^{2}\phantom{-;x^n}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{\phantom{;}2x^{2}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}2x^{2}-2x\phantom{;}-;x^n-;x^n-;x^n;}-2x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}2x\phantom{;}-2\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-8\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+x^{3}-2x^{2}-2x-2+\frac{-8}{x-1}$