$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{-8x^{2}+24x\phantom{;}-72\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}-8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{\phantom{;}8x^{3}+24x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}8x^{3}+24x^{2};}\phantom{;}24x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{-24x^{2}-72x\phantom{;}\phantom{-;x^n}}\\\phantom{;-24x^{2}-72x\phantom{;}-;x^n;}-72x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}72x\phantom{;}+216\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}72x\phantom{;}+216\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}216\phantom{;}\phantom{;}\\\end{array}$

$-8x^{2}+24x-72+\frac{216}{x+3}$