$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{-4x^{3}+8x^{2}-24x\phantom{;}+64\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}-4x^{4}-4x^{3}\phantom{-;x^n}-8x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{\phantom{;}4x^{4}+12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}4x^{4}+12x^{3};}\phantom{;}8x^{3}\phantom{-;x^n}-8x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{-8x^{3}-24x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-8x^{3}-24x^{2}-;x^n;}-24x^{2}-8x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}24x^{2}+72x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}24x^{2}+72x\phantom{;}-;x^n-;x^n;}\phantom{;}64x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{-64x\phantom{;}-192\phantom{;}\phantom{;}}\\\phantom{;;;-64x\phantom{;}-192\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-191\phantom{;}\phantom{;}\\\end{array}$

$-4x^{3}+8x^{2}-24x+64+\frac{-191}{x+3}$