$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+4;}{\phantom{;}x^{2}-x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+4\overline{\smash{)}\phantom{;}x^{3}+3x^{2}\phantom{-;x^n}+12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+4;}\underline{-x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-4x^{2};}-x^{2}\phantom{-;x^n}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n;}\underline{\phantom{;}x^{2}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{2}+4x\phantom{;}-;x^n;}\phantom{;}4x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n;}\underline{-4x\phantom{;}-16\phantom{;}\phantom{;}}\\\phantom{;;-4x\phantom{;}-16\phantom{;}\phantom{;}-;x^n-;x^n;}-4\phantom{;}\phantom{;}\\\end{array}$

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