23. Simplify the expression: $$\frac{25a^2 - 36b^2}{55a^2 - 66ab}$$

Solution:

1. Factor the numerator: The numerator is a difference of squares: $$25a^2 - 36b^2 = (5a)^2 - (6b)^2 = (5a - 6b)(5a + 6b)$$.
2. Factor the denominator: The denominator has a common factor of $$11a$$: $$55a^2 - 66ab = 11a(5a - 6b)$$.
3. Simplify the fraction: $$\frac{(5a - 6b)(5a + 6b)}{11a(5a - 6b)}$$.
4. Cancel out the common term $$(5a - 6b)$$: $$\frac{5a + 6b}{11a}$$.

Answer: $$\frac{5a + 6b}{11a}$$