$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}2x^{2}-7x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}2x^{3}-3x^{2}-5x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-2x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{3}-4x^{2};}-7x^{2}-5x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}7x^{2}+14x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}7x^{2}+14x\phantom{;}-;x^n;}\phantom{;}9x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-9x\phantom{;}-18\phantom{;}\phantom{;}}\\\phantom{;;-9x\phantom{;}-18\phantom{;}\phantom{;}-;x^n-;x^n;}-14\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}-7x+9+\frac{-14}{x+2}$