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

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