$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{-3x^{3}+9x^{2}-21x\phantom{;}+62\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}-3x^{4}\phantom{-;x^n}+6x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{\phantom{;}3x^{4}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}3x^{4}+9x^{3};}\phantom{;}9x^{3}+6x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{-9x^{3}-27x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-9x^{3}-27x^{2}-;x^n;}-21x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}21x^{2}+63x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}21x^{2}+63x\phantom{;}-;x^n-;x^n;}\phantom{;}62x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{-62x\phantom{;}-186\phantom{;}\phantom{;}}\\\phantom{;;;-62x\phantom{;}-186\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-184\phantom{;}\phantom{;}\\\end{array}$

$-3x^{3}+9x^{2}-21x+62+\frac{-184}{x+3}$