$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}-3;}{\phantom{;}2x^{2}-8x\phantom{;}+17\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+x\phantom{;}-3\overline{\smash{)}\phantom{;}2x^{4}-6x^{3}+3x^{2}-4x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-3;}\underline{-2x^{4}-2x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-2x^{3}+6x^{2};}-8x^{3}+9x^{2}-4x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-3-;x^n;}\underline{\phantom{;}8x^{3}+8x^{2}-24x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}8x^{3}+8x^{2}-24x\phantom{;}-;x^n;}\phantom{;}17x^{2}-28x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-3-;x^n-;x^n;}\underline{-17x^{2}-17x\phantom{;}+51\phantom{;}\phantom{;}}\\\phantom{;;-17x^{2}-17x\phantom{;}+51\phantom{;}\phantom{;}-;x^n-;x^n;}-45x\phantom{;}+49\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}-8x+17+\frac{-45x+49}{x^2+x-3}$