$\begin{array}{l}\phantom{\phantom{;}y^{2}+3y\phantom{;}-2;}{\phantom{;}y\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}y^{2}+3y\phantom{;}-2\overline{\smash{)}\phantom{;}y^{3}\phantom{-;x^n}-6y\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}y^{2}+3y\phantom{;}-2;}\underline{-y^{3}-3y^{2}+2y\phantom{;}\phantom{-;x^n}}\\\phantom{-y^{3}-3y^{2}+2y\phantom{;};}-3y^{2}-4y\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}y^{2}+3y\phantom{;}-2-;x^n;}\underline{\phantom{;}3y^{2}+9y\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}3y^{2}+9y\phantom{;}-6\phantom{;}\phantom{;}-;x^n;}\phantom{;}5y\phantom{;}-1\phantom{;}\phantom{;}\\\end{array}$

$y-3+\frac{5y-1}{y^2+3y-2}$