$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{2}-6x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{3}-4x^{2}-4x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-2x^{2};}-6x^{2}-4x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}6x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{2}+12x\phantom{;}-;x^n;}\phantom{;}8x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-8x\phantom{;}-16\phantom{;}\phantom{;}}\\\phantom{;;-8x\phantom{;}-16\phantom{;}\phantom{;}-;x^n-;x^n;}-14\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-6x+8+\frac{-14}{x+2}$