$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}3x^{3}+8x^{2}+24x\phantom{;}+72\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}3x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-3x^{4}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+9x^{3};}\phantom{;}8x^{3}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-8x^{3}+24x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-8x^{3}+24x^{2}-;x^n;}\phantom{;}24x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-24x^{2}+72x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-24x^{2}+72x\phantom{;}-;x^n-;x^n;}\phantom{;}72x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-72x\phantom{;}+216\phantom{;}\phantom{;}}\\\phantom{;;;-72x\phantom{;}+216\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}218\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}+8x^{2}+24x+72+\frac{218}{x-3}$