$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}2x^{2}+x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}2x^{3}+3x^{2}+5x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-2x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{3}-2x^{2};}\phantom{;}x^{2}+5x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;-x^{2}-x\phantom{;}-;x^n;}\phantom{;}4x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-4x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;;-4x\phantom{;}-4\phantom{;}\phantom{;}-;x^n-;x^n;}-6\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}+x+4+\frac{-6}{x+1}$