$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}3x^{2}-7x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}3x^{3}-x^{2}+x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-3x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}-6x^{2};}-7x^{2}+x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}7x^{2}+14x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}7x^{2}+14x\phantom{;}-;x^n;}\phantom{;}15x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-15x\phantom{;}-30\phantom{;}\phantom{;}}\\\phantom{;;-15x\phantom{;}-30\phantom{;}\phantom{;}-;x^n-;x^n;}-32\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}-7x+15+\frac{-32}{x+2}$