$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}+1;}{\phantom{;}4x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+x\phantom{;}+1\overline{\smash{)}\phantom{;}4x^{3}-2x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+1;}\underline{-4x^{3}-4x^{2}-4x\phantom{;}\phantom{-;x^n}}\\\phantom{-4x^{3}-4x^{2}-4x\phantom{;};}-6x^{2}-3x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+1-;x^n;}\underline{\phantom{;}6x^{2}+6x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}6x^{2}+6x\phantom{;}+6\phantom{;}\phantom{;}-;x^n;}\phantom{;}3x\phantom{;}+5\phantom{;}\phantom{;}\\\end{array}$

$4x-6+\frac{3x+5}{x^2+x+1}$