$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{2}-3x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{3}-2x^{2}-11x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-x^{2};}-3x^{2}-11x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}3x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{2}+3x\phantom{;}-;x^n;}-8x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}8x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}8x\phantom{;}+8\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}20\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-3x-8+\frac{20}{x+1}$