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

$x^{2}-2x+4+\frac{-3}{x+2}$