Answer
$\dfrac{1}{10y^{n+1}+30y}$
Work Step by Step
Factor the numerators and the denominators, when needed to have:
$\\=\dfrac{y^{2n}+9}{10y} \cdot \dfrac{y^n-3}{(y^{2n}-9)(y^{2n}+9)}
\\=\dfrac{y^{2n}+9}{10y} \cdot \dfrac{y^n-3}{(y^n-3)(y^n+3)(y^{2n}+9)}$
Cancel the common factors to have:
$\require{cancel}\\=\dfrac{\cancel{y^{2n}+9}}{10y} \cdot \dfrac{\cancel{y^n-3}}{\cancel{(y^n-3)}(y^n+3)\cancel{(y^{2n}+9)}}
\\=\dfrac{1}{10y(y^n+3)}
\\=\dfrac{1}{10y^{n+1}+30y}$
