$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}3x^{5}+2x^{4}-4x^{3}+8x^{2}-31x\phantom{;}+60\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}3x^{6}+8x^{5}\phantom{-;x^n}\phantom{-;x^n}-15x^{2}-2x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-3x^{6}-6x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{6}-6x^{5};}\phantom{;}2x^{5}\phantom{-;x^n}\phantom{-;x^n}-15x^{2}-2x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{-2x^{5}-4x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{5}-4x^{4}-;x^n;}-4x^{4}\phantom{-;x^n}-15x^{2}-2x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}4x^{4}+8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}4x^{4}+8x^{3}-;x^n-;x^n;}\phantom{;}8x^{3}-15x^{2}-2x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{-8x^{3}-16x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-8x^{3}-16x^{2}-;x^n-;x^n-;x^n;}-31x^{2}-2x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}31x^{2}+62x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;\phantom{;}31x^{2}+62x\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}60x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-60x\phantom{;}-120\phantom{;}\phantom{;}}\\\phantom{;;;;;-60x\phantom{;}-120\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}-115\phantom{;}\phantom{;}\\\end{array}$

$3x^{5}+2x^{4}-4x^{3}+8x^{2}-31x+60+\frac{-115}{x+2}$