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

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