$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{3}+3x^{2}-6x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{4}+5x^{3}\phantom{-;x^n}-8x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{3};}\phantom{;}3x^{3}\phantom{-;x^n}-8x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{-3x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{3}-6x^{2}-;x^n;}-6x^{2}-8x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}6x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}6x^{2}+12x\phantom{;}-;x^n-;x^n;}\phantom{;}4x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{-4x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;;;-4x\phantom{;}-8\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}2\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+3x^{2}-6x+4+\frac{2}{x+2}$