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

$2x^{3}-3x^{2}+4x-3+\frac{2}{x+1}$