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

$x^{4}+x^{3}+3x^{2}+3x+3+\frac{5}{x-1}$