$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}3x^{3}-6x^{2}+15x\phantom{;}-29\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}3x^{4}\phantom{-;x^n}+3x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-3x^{4}-6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-6x^{3};}-6x^{3}+3x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}6x^{3}+12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{3}+12x^{2}-;x^n;}\phantom{;}15x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-15x^{2}-30x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-15x^{2}-30x\phantom{;}-;x^n-;x^n;}-29x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}29x\phantom{;}+58\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}29x\phantom{;}+58\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}53\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-6x^{2}+15x-29+\frac{53}{x+2}$