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

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