$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}3x^{3}-6x^{2}+11x\phantom{;}-22\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}3x^{4}\phantom{-;x^n}-x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-3x^{4}-6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-6x^{3};}-6x^{3}-x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}6x^{3}+12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{3}+12x^{2}-;x^n;}\phantom{;}11x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-11x^{2}-22x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-11x^{2}-22x\phantom{;}-;x^n-;x^n;}-22x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}22x\phantom{;}+44\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}22x\phantom{;}+44\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}43\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-6x^{2}+11x-22+\frac{43}{x+2}$