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

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