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

$-x^{2}+x-5+\frac{8}{x+1}$