To simplify the expression (4a^2 - 12ab + 9b^2) / (4a^2 - 9b^2), we need to factor the numerator and the denominator.

Numerator:
4a^2 - 12ab + 9b^2
= (2a - 3b)^2

Denominator:
4a^2 - 9b^2
= (2a + 3b)(2a - 3b)

Now, we can rewrite the expression as ((2a - 3b)^2) / ((2a + 3b)(2a - 3b)).

Since the numerator and the denominator have a common factor of (2a - 3b), we can cancel it out to simplify the expression to 1 / (2a + 3b).

Therefore, the simplified form of the expression (4a^2 - 12ab + 9b^2) / (4a^2 - 9b^2) is 1 / (2a + 3b).