$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}2x^{3}-x^{2}-4x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}2x^{4}+3x^{3}-6x^{2}\phantom{-;x^n}+7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-2x^{4}-4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-4x^{3};}-x^{3}-6x^{2}\phantom{-;x^n}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}+2x^{2}-;x^n;}-4x^{2}\phantom{-;x^n}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}4x^{2}+8x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}4x^{2}+8x\phantom{;}-;x^n-;x^n;}\phantom{;}8x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{-8x\phantom{;}-16\phantom{;}\phantom{;}}\\\phantom{;;;-8x\phantom{;}-16\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-9\phantom{;}\phantom{;}\\\end{array}$

$2x^{3}-x^{2}-4x+8+\frac{-9}{x+2}$