1. **State the problem:** Simplify the expression $\frac{2x + by + a}{15y} \div \frac{3y^2}{2y + b}$. 2. **Rewrite the division as multiplication:** $$\frac{2x + by + a}{15y} \times \frac{2y + b}{3y^2}$$ 3. **Multiply the numerators and denominators:** $$\frac{(2x + by + a)(2y + b)}{15y \times 3y^2} = \frac{(2x + by + a)(2y + b)}{45y^3}$$ 4. **Final simplified form:** $$\frac{(2x + by + a)(2y + b)}{45y^3}$$ This is the simplified expression since no further factorization or cancellation is possible without additional information about variables.