$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}3x^{2}-5x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}3x^{3}+x^{2}-4x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-3x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}-6x^{2};}-5x^{2}-4x\phantom{;}-12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}5x^{2}+10x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{2}+10x\phantom{;}-;x^n;}\phantom{;}6x\phantom{;}-12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-6x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;;-6x\phantom{;}-12\phantom{;}\phantom{;}-;x^n-;x^n;}-24\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}-5x+6+\frac{-24}{x+2}$