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

$x^{3}-6x^{2}+6x-8+\frac{6}{x+1}$