24. Simplify the expression: $$\frac{66xy + 77y^2}{36x^2 + 84xy + 49y^2}$$

Solution:

1. Factor the numerator: The numerator has a common factor of $$11y$$: $$66xy + 77y^2 = 11y(6x + 7y)$$.
2. Factor the denominator: The denominator is a perfect square trinomial: $$36x^2 + 84xy + 49y^2 = (6x)^2 + 2(6x)(7y) + (7y)^2 = (6x + 7y)^2$$.
3. Simplify the fraction: $$\frac{11y(6x + 7y)}{(6x + 7y)^2}$$.
4. Cancel out the common term $$(6x + 7y)$$: $$\frac{11y}{6x + 7y}$$.

Answer: $$\frac{11y}{6x + 7y}$$