$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}2x^{2}-9x\phantom{;}+24\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}2x^{3}-5x^{2}+6x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-2x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{3}-4x^{2};}-9x^{2}+6x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}9x^{2}+18x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}9x^{2}+18x\phantom{;}-;x^n;}\phantom{;}24x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-24x\phantom{;}-48\phantom{;}\phantom{;}}\\\phantom{;;-24x\phantom{;}-48\phantom{;}\phantom{;}-;x^n-;x^n;}-51\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}-9x+24+\frac{-51}{x+2}$