$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}4x^{2}-8x\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}4x^{3}\phantom{-;x^n}\phantom{-;x^n}-9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-4x^{3}-8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}-8x^{2};}-8x^{2}\phantom{-;x^n}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}8x^{2}+16x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}8x^{2}+16x\phantom{;}-;x^n;}\phantom{;}16x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-16x\phantom{;}-32\phantom{;}\phantom{;}}\\\phantom{;;-16x\phantom{;}-32\phantom{;}\phantom{;}-;x^n-;x^n;}-41\phantom{;}\phantom{;}\\\end{array}$

$4x^{2}-8x+16+\frac{-41}{x+2}$