$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}2x^{2}-8x\phantom{;}+21\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}2x^{3}-4x^{2}+5x\phantom{;}-13\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-2x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{3}-4x^{2};}-8x^{2}+5x\phantom{;}-13\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}8x^{2}+16x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}8x^{2}+16x\phantom{;}-;x^n;}\phantom{;}21x\phantom{;}-13\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-21x\phantom{;}-42\phantom{;}\phantom{;}}\\\phantom{;;-21x\phantom{;}-42\phantom{;}\phantom{;}-;x^n-;x^n;}-55\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}-8x+21+\frac{-55}{x+2}$