Решение:

$$\frac{3x}{y+1} : \frac{y+y^2}{9} = \frac{3x}{y+1} \cdot \frac{9}{y+y^2} = \frac{3x \cdot 9}{(y+1) \cdot (y+y^2)} = \frac{27x}{(y+1) \cdot y \cdot (1+y)} = \frac{27x}{y(y+1)^2}$$

Ответ: $$\frac{27x}{y(y+1)^2}$$