21. Simplify the expression: $$\frac{144a^2 - 25b^2}{25b^2 - 120ab + 144a^2}$$

Solution:

1. Factor the numerator: The numerator is a difference of squares, $$144a^2 - 25b^2 = (12a)^2 - (5b)^2 = (12a - 5b)(12a + 5b)$$.
2. Factor the denominator: The denominator is a perfect square trinomial, $$25b^2 - 120ab + 144a^2 = (5b - 12a)^2 = (5b - 12a)(5b - 12a)$$.
3. Simplify the fraction: $$\frac{(12a - 5b)(12a + 5b)}{(5b - 12a)^2}$$. Notice that $$(5b - 12a) = -(12a - 5b)$$. So, $$(5b - 12a)^2 = (-(12a - 5b))^2 = (12a - 5b)^2$$.
4. Substitute back: $$\frac{(12a - 5b)(12a + 5b)}{(12a - 5b)^2} = \frac{12a + 5b}{12a - 5b}$$.

Answer: $$\frac{12a + 5b}{12a - 5b}$$