$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}2x^{3}+2x^{2}-2x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}2x^{4}+4x^{3}\phantom{-;x^n}+3x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-2x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-2x^{3};}\phantom{;}2x^{3}\phantom{-;x^n}+3x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-2x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{3}-2x^{2}-;x^n;}-2x^{2}+3x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}2x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}2x^{2}+2x\phantom{;}-;x^n-;x^n;}\phantom{;}5x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-5x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;;;-5x\phantom{;}-5\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-10\phantom{;}\phantom{;}\\\end{array}$

$2x^{3}+2x^{2}-2x+5+\frac{-10}{x+1}$