$\begin{array}{l}\phantom{\phantom{;}x^{3}-x\phantom{;}+2;}{-6x^{3}+12x^{2}-6x\phantom{;}+27\phantom{;}\phantom{;}}\\\phantom{;}x^{3}-x\phantom{;}+2\overline{\smash{)}-6x^{6}+12x^{5}\phantom{-;x^n}+3x^{3}\phantom{-;x^n}-4x\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{3}-x\phantom{;}+2;}\underline{\phantom{;}6x^{6}\phantom{-;x^n}-6x^{4}+12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}6x^{6}-6x^{4}+12x^{3};}\phantom{;}12x^{5}-6x^{4}+15x^{3}\phantom{-;x^n}-4x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{3}-x\phantom{;}+2-;x^n;}\underline{-12x^{5}\phantom{-;x^n}+12x^{3}-24x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-12x^{5}+12x^{3}-24x^{2}-;x^n;}-6x^{4}+27x^{3}-24x^{2}-4x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{3}-x\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}6x^{4}\phantom{-;x^n}-6x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}6x^{4}-6x^{2}+12x\phantom{;}-;x^n-;x^n;}\phantom{;}27x^{3}-30x^{2}+8x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{3}-x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{-27x^{3}\phantom{-;x^n}+27x\phantom{;}-54\phantom{;}\phantom{;}}\\\phantom{;;;-27x^{3}+27x\phantom{;}-54\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-30x^{2}+35x\phantom{;}-38\phantom{;}\phantom{;}\\\end{array}$

$-6x^{3}+12x^{2}-6x+27+\frac{-30x^{2}+35x-38}{x^3-x+2}$