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

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