$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;}+1;}{\phantom{;}5x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}+1\overline{\smash{)}\phantom{;}5x^{3}+x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1;}\underline{-5x^{3}+5x^{2}-5x\phantom{;}\phantom{-;x^n}}\\\phantom{-5x^{3}+5x^{2}-5x\phantom{;};}\phantom{;}6x^{2}-5x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1-;x^n;}\underline{-6x^{2}+6x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;-6x^{2}+6x\phantom{;}-6\phantom{;}\phantom{;}-;x^n;}\phantom{;}x\phantom{;}-9\phantom{;}\phantom{;}\\\end{array}$

$5x+6+\frac{x-9}{x^2-x+1}$