$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}3x^{2}-10x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}3x^{3}-x^{2}-22x\phantom{;}-24\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-3x^{3}-9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}-9x^{2};}-10x^{2}-22x\phantom{;}-24\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}10x^{2}+30x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}10x^{2}+30x\phantom{;}-;x^n;}\phantom{;}8x\phantom{;}-24\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-8x\phantom{;}-24\phantom{;}\phantom{;}}\\\phantom{;;-8x\phantom{;}-24\phantom{;}\phantom{;}-;x^n-;x^n;}-48\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}-10x+8+\frac{-48}{x+3}$