$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}6x^{3}-6x^{2}+7x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}6x^{4}\phantom{-;x^n}+x^{2}+4x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-6x^{4}-6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{4}-6x^{3};}-6x^{3}+x^{2}+4x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}6x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{3}+6x^{2}-;x^n;}\phantom{;}7x^{2}+4x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-7x^{2}-7x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-7x^{2}-7x\phantom{;}-;x^n-;x^n;}-3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}3x\phantom{;}+3\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}5\phantom{;}\phantom{;}\\\end{array}$

$6x^{3}-6x^{2}+7x-3+\frac{5}{x+1}$