$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;}+1;}{\phantom{;}x^{2}-2x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{4}-3x^{3}-4x^{2}-x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1;}\underline{-x^{4}+x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+x^{3}-x^{2};}-2x^{3}-5x^{2}-x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1-;x^n;}\underline{\phantom{;}2x^{3}-2x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{3}-2x^{2}+2x\phantom{;}-;x^n;}-7x^{2}+x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}7x^{2}-7x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}7x^{2}-7x\phantom{;}+7\phantom{;}\phantom{;}-;x^n-;x^n;}-6x\phantom{;}+8\phantom{;}\phantom{;}\\\end{array}$

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