$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}3x^{2}-6x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}3x^{3}\phantom{-;x^n}-10x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-3x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}-6x^{2};}-6x^{2}-10x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}6x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{2}+12x\phantom{;}-;x^n;}\phantom{;}2x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-2x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;;-2x\phantom{;}-4\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}5\phantom{;}\phantom{;}\\\end{array}$

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