$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{2}-5x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{3}-2x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-3x^{2};}-5x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}5x^{2}+15x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{2}+15x\phantom{;}-;x^n;}\phantom{;}15x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-15x\phantom{;}-45\phantom{;}\phantom{;}}\\\phantom{;;-15x\phantom{;}-45\phantom{;}\phantom{;}-;x^n-;x^n;}-48\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-5x+15+\frac{-48}{x+3}$