$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+4;}{-x^{2}+9x\phantom{;}-44\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+4\overline{\smash{)}-x^{3}+5x^{2}-8x\phantom{;}-50\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+4;}\underline{\phantom{;}x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{3}+4x^{2};}\phantom{;}9x^{2}-8x\phantom{;}-50\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n;}\underline{-9x^{2}-36x\phantom{;}\phantom{-;x^n}}\\\phantom{;-9x^{2}-36x\phantom{;}-;x^n;}-44x\phantom{;}-50\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+4-;x^n-;x^n;}\underline{\phantom{;}44x\phantom{;}+176\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}44x\phantom{;}+176\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}126\phantom{;}\phantom{;}\\\end{array}$

$-x^{2}+9x-44+\frac{126}{x+4}$