$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+4;}{\phantom{;}x^{3}+2x^{2}-8x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+4\overline{\smash{)}\phantom{;}x^{4}+6x^{3}\phantom{-;x^n}-24x\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+4;}\underline{-x^{4}-4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-4x^{3};}\phantom{;}2x^{3}\phantom{-;x^n}-24x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n;}\underline{-2x^{3}-8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{3}-8x^{2}-;x^n;}-8x^{2}-24x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n;}\underline{\phantom{;}8x^{2}+32x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}8x^{2}+32x\phantom{;}-;x^n-;x^n;}\phantom{;}8x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n-;x^n;}\underline{-8x\phantom{;}-32\phantom{;}\phantom{;}}\\\phantom{;;;-8x\phantom{;}-32\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-16\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+2x^{2}-8x+8+\frac{-16}{x+4}$