$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{3}-2x^{2}+3x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}-x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{3};}-2x^{3}-x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}2x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{3}+4x^{2}-;x^n;}\phantom{;}3x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-3x^{2}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-3x^{2}-6x\phantom{;}-;x^n-;x^n;}-6x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}6x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}6x\phantom{;}+12\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}15\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-2x^{2}+3x-6+\frac{15}{x+2}$