$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}3x^{3}-11x^{2}+24x\phantom{;}-55\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}3x^{4}-5x^{3}+2x^{2}-7x\phantom{;}+11\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-3x^{4}-6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-6x^{3};}-11x^{3}+2x^{2}-7x\phantom{;}+11\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}11x^{3}+22x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}11x^{3}+22x^{2}-;x^n;}\phantom{;}24x^{2}-7x\phantom{;}+11\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-24x^{2}-48x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-24x^{2}-48x\phantom{;}-;x^n-;x^n;}-55x\phantom{;}+11\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}55x\phantom{;}+110\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}55x\phantom{;}+110\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}121\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-11x^{2}+24x-55+\frac{121}{x+2}$