$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{2}+11x\phantom{;}-31\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{3}+12x^{2}-20x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-x^{2};}\phantom{;}11x^{2}-20x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-11x^{2}-11x\phantom{;}\phantom{-;x^n}}\\\phantom{;-11x^{2}-11x\phantom{;}-;x^n;}-31x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}31x\phantom{;}+31\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}31x\phantom{;}+31\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}38\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+11x-31+\frac{38}{x+1}$