$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{3}-x^{2}+3x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{4}+2x^{3}\phantom{-;x^n}+15x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-3x^{3};}-x^{3}\phantom{-;x^n}+15x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}+3x^{2}-;x^n;}\phantom{;}3x^{2}+15x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-3x^{2}-9x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-3x^{2}-9x\phantom{;}-;x^n-;x^n;}\phantom{;}6x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{-6x\phantom{;}-18\phantom{;}\phantom{;}}\\\phantom{;;;-6x\phantom{;}-18\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-10\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-x^{2}+3x+6+\frac{-10}{x+3}$