$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}6x^{3}-15x^{2}+30x\phantom{;}-60\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}6x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-6x^{4}-12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{4}-12x^{3};}-15x^{3}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}15x^{3}+30x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}15x^{3}+30x^{2}-;x^n;}\phantom{;}30x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-30x^{2}-60x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-30x^{2}-60x\phantom{;}-;x^n-;x^n;}-60x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}60x\phantom{;}+120\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}60x\phantom{;}+120\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}121\phantom{;}\phantom{;}\\\end{array}$

$6x^{3}-15x^{2}+30x-60+\frac{121}{x+2}$