$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}4x^{5}+4x^{4}+x^{3}+x^{2}+2x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}4x^{6}\phantom{-;x^n}-3x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}+5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-4x^{6}+4x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{6}+4x^{5};}\phantom{;}4x^{5}-3x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-4x^{5}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{5}+4x^{4}-;x^n;}\phantom{;}x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{-x^{4}+x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-x^{4}+x^{3}-;x^n-;x^n;}\phantom{;}x^{3}+x^{2}\phantom{-;x^n}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{-x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-x^{3}+x^{2}-;x^n-;x^n-;x^n;}\phantom{;}2x^{2}\phantom{-;x^n}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n-;x^n;}\underline{-2x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;-2x^{2}+2x\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}2x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-2x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;;;;;-2x\phantom{;}+2\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}7\phantom{;}\phantom{;}\\\end{array}$

$4x^{5}+4x^{4}+x^{3}+x^{2}+2x+2+\frac{7}{x-1}$