$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}2x^{3}-3x^{2}+6x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}2x^{4}+x^{3}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-2x^{4}-4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-4x^{3};}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}3x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{3}+6x^{2}-;x^n;}\phantom{;}6x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-6x^{2}-12x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-6x^{2}-12x\phantom{;}-;x^n-;x^n;}-12x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}12x\phantom{;}+24\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}12x\phantom{;}+24\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}23\phantom{;}\phantom{;}\\\end{array}$

$2x^{3}-3x^{2}+6x-12+\frac{23}{x+2}$