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

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