$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{2}-4x\phantom{;}+24\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{3}-2x^{2}+16x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-2x^{2};}-4x^{2}+16x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}4x^{2}+8x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{2}+8x\phantom{;}-;x^n;}\phantom{;}24x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-24x\phantom{;}-48\phantom{;}\phantom{;}}\\\phantom{;;-24x\phantom{;}-48\phantom{;}\phantom{;}-;x^n-;x^n;}-56\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-4x+24+\frac{-56}{x+2}$