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

$6x-8+\frac{2x+7}{x^2+x+1}$