$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}3x^{2}-7x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}3x^{3}-x^{2}-4x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-3x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}-6x^{2};}-7x^{2}-4x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}7x^{2}+14x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}7x^{2}+14x\phantom{;}-;x^n;}\phantom{;}10x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-10x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{;;-10x\phantom{;}-20\phantom{;}\phantom{;}-;x^n-;x^n;}-8\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}-7x+10+\frac{-8}{x+2}$