$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{3}-6x^{2}+12x\phantom{;}-22\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{4}-4x^{3}\phantom{-;x^n}+2x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{3};}-6x^{3}\phantom{-;x^n}+2x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}6x^{3}+12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{3}+12x^{2}-;x^n;}\phantom{;}12x^{2}+2x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-12x^{2}-24x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-12x^{2}-24x\phantom{;}-;x^n-;x^n;}-22x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}22x\phantom{;}+44\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}22x\phantom{;}+44\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}37\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-6x^{2}+12x-22+\frac{37}{x+2}$