$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;}+1;}{\phantom{;}2x^{2}+12x\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}+1\overline{\smash{)}\phantom{;}2x^{4}+10x^{3}+6x^{2}+3x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1;}\underline{-2x^{4}+2x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+2x^{3}-2x^{2};}\phantom{;}12x^{3}+4x^{2}+3x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1-;x^n;}\underline{-12x^{3}+12x^{2}-12x\phantom{;}\phantom{-;x^n}}\\\phantom{;-12x^{3}+12x^{2}-12x\phantom{;}-;x^n;}\phantom{;}16x^{2}-9x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+1-;x^n-;x^n;}\underline{-16x^{2}+16x\phantom{;}-16\phantom{;}\phantom{;}}\\\phantom{;;-16x^{2}+16x\phantom{;}-16\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}7x\phantom{;}-15\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}+12x+16+\frac{7x-15}{x^2-x+1}$