$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}6x^{3}+6x^{2}-9x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}6x^{4}\phantom{-;x^n}-15x^{2}-3x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-6x^{4}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{4}+6x^{3};}\phantom{;}6x^{3}-15x^{2}-3x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-6x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-6x^{3}+6x^{2}-;x^n;}-9x^{2}-3x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{\phantom{;}9x^{2}-9x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}9x^{2}-9x\phantom{;}-;x^n-;x^n;}-12x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{\phantom{;}12x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}12x\phantom{;}-12\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-2\phantom{;}\phantom{;}\\\end{array}$

$6x^{3}+6x^{2}-9x-12+\frac{-2}{x-1}$