$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{4}+2x^{3}-11x^{2}+11x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{5}+3x^{4}-9x^{3}\phantom{-;x^n}+7x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{5}-x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-x^{4};}\phantom{;}2x^{4}-9x^{3}\phantom{-;x^n}+7x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-2x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{4}-2x^{3}-;x^n;}-11x^{3}\phantom{-;x^n}+7x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}11x^{3}+11x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}11x^{3}+11x^{2}-;x^n-;x^n;}\phantom{;}11x^{2}+7x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-11x^{2}-11x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-11x^{2}-11x\phantom{;}-;x^n-;x^n-;x^n;}-4x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}4x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}4x\phantom{;}+4\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}1\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+2x^{3}-11x^{2}+11x-4+\frac{1}{x+1}$