$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}5x^{2}-15x\phantom{;}+48\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}5x^{3}\phantom{-;x^n}+3x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-5x^{3}-15x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-5x^{3}-15x^{2};}-15x^{2}+3x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}15x^{2}+45x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}15x^{2}+45x\phantom{;}-;x^n;}\phantom{;}48x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-48x\phantom{;}-144\phantom{;}\phantom{;}}\\\phantom{;;-48x\phantom{;}-144\phantom{;}\phantom{;}-;x^n-;x^n;}-138\phantom{;}\phantom{;}\\\end{array}$

$5x^{2}-15x+48+\frac{-138}{x+3}$