$\begin{array}{l}\phantom{\phantom{;}y\phantom{;}+3;}{\phantom{;}y^{2}-3y\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}y\phantom{;}+3\overline{\smash{)}\phantom{;}y^{3}\phantom{-;x^n}-3y\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}y\phantom{;}+3;}\underline{-y^{3}-3y^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-y^{3}-3y^{2};}-3y^{2}-3y\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}+3-;x^n;}\underline{\phantom{;}3y^{2}+9y\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3y^{2}+9y\phantom{;}-;x^n;}\phantom{;}6y\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}+3-;x^n-;x^n;}\underline{-6y\phantom{;}-18\phantom{;}\phantom{;}}\\\phantom{;;-6y\phantom{;}-18\phantom{;}\phantom{;}-;x^n-;x^n;}-12\phantom{;}\phantom{;}\\\end{array}$

$y^{2}-3y+6+\frac{-12}{y+3}$