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

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