Answer
$$\frac{\left(5y+1\right)\left(y+1\right)}{3y^2+6y}$$
Work Step by Step
Recall, one never divides by a fraction. Rather, if we want to divide by a fraction, we multiply by the reciprocal of the fraction. Recall, the reciprocal of a fraction is that fraction with the numerator and the denominator switched. Thus, we find:
$$ \frac{25y^2-1}{9y^2-6y}\times \frac{3y^2+y-2}{5y^2+9y-2}\\ \frac{\left(5y+1\right)\left(5y-1\right)\left(y+1\right)}{3y\left(5y-1\right)\left(y+2\right)}\\ \frac{\left(5y+1\right)\left(y+1\right)}{3y^2+6y}$$
