$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}2x^{3}-8x^{2}+16x\phantom{;}-31\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}2x^{4}-4x^{3}\phantom{-;x^n}+x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-2x^{4}-4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-4x^{3};}-8x^{3}\phantom{-;x^n}+x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}8x^{3}+16x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}8x^{3}+16x^{2}-;x^n;}\phantom{;}16x^{2}+x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-16x^{2}-32x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-16x^{2}-32x\phantom{;}-;x^n-;x^n;}-31x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}31x\phantom{;}+62\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}31x\phantom{;}+62\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}59\phantom{;}\phantom{;}\\\end{array}$

$2x^{3}-8x^{2}+16x-31+\frac{59}{x+2}$