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

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