$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{-2x^{3}+6x^{2}-2x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}-2x^{4}\phantom{-;x^n}+16x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{\phantom{;}2x^{4}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}2x^{4}+6x^{3};}\phantom{;}6x^{3}+16x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{-6x^{3}-18x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-6x^{3}-18x^{2}-;x^n;}-2x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}2x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}2x^{2}+6x\phantom{;}-;x^n-;x^n;}\phantom{;}6x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{-6x\phantom{;}-18\phantom{;}\phantom{;}}\\\phantom{;;;-6x\phantom{;}-18\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-21\phantom{;}\phantom{;}\\\end{array}$

$-2x^{3}+6x^{2}-2x+6+\frac{-21}{x+3}$