$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{3}-7x^{2}+14x\phantom{;}-24\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{4}-5x^{3}\phantom{-;x^n}+4x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{3};}-7x^{3}\phantom{-;x^n}+4x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}7x^{3}+14x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}7x^{3}+14x^{2}-;x^n;}\phantom{;}14x^{2}+4x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-14x^{2}-28x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-14x^{2}-28x\phantom{;}-;x^n-;x^n;}-24x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}24x\phantom{;}+48\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}24x\phantom{;}+48\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}44\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-7x^{2}+14x-24+\frac{44}{x+2}$