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

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