$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}3x^{5}+3x^{4}+8x^{3}+8x^{2}+6x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}3x^{6}\phantom{-;x^n}+5x^{4}\phantom{-;x^n}-2x^{2}+x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-3x^{6}+3x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{6}+3x^{5};}\phantom{;}3x^{5}+5x^{4}\phantom{-;x^n}-2x^{2}+x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-3x^{5}+3x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{5}+3x^{4}-;x^n;}\phantom{;}8x^{4}\phantom{-;x^n}-2x^{2}+x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{-8x^{4}+8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-8x^{4}+8x^{3}-;x^n-;x^n;}\phantom{;}8x^{3}-2x^{2}+x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{-8x^{3}+8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-8x^{3}+8x^{2}-;x^n-;x^n-;x^n;}\phantom{;}6x^{2}+x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n-;x^n;}\underline{-6x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;-6x^{2}+6x\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}7x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-7x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;;;;;-7x\phantom{;}+7\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}11\phantom{;}\phantom{;}\\\end{array}$

$3x^{5}+3x^{4}+8x^{3}+8x^{2}+6x+7+\frac{11}{x-1}$