Verified answer

[tex]\displaystyle\bf\\\frac{x+y}{3y} :\frac{x^{2} -y^{2} }{9y^{2} } =\frac{x+y}{3y} :\frac{(x-y)(x+y) }{9y^{2} } =\frac{x+y}{3y} \cdot\frac{9y^{2} }{(x-y)(x+y)} =\\\\\\=\frac{3y}{x-y}[/tex]