$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+4;}{\phantom{;}x^{2}+x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+4\overline{\smash{)}\phantom{;}x^{3}+5x^{2}-4x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+4;}\underline{-x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-4x^{2};}\phantom{;}x^{2}-4x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n;}\underline{-x^{2}-4x\phantom{;}\phantom{-;x^n}}\\\phantom{;-x^{2}-4x\phantom{;}-;x^n;}-8x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n;}\underline{\phantom{;}8x\phantom{;}+32\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}8x\phantom{;}+32\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}12\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+x-8+\frac{12}{x+4}$