$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{2}+4x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{3}+6x^{2}+7x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-2x^{2};}\phantom{;}4x^{2}+7x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{-4x^{2}-8x\phantom{;}\phantom{-;x^n}}\\\phantom{;-4x^{2}-8x\phantom{;}-;x^n;}-x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}x\phantom{;}+2\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}4\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+4x-1+\frac{4}{x+2}$