To simplify the expression (4a^2 - 12ab + 9b^2) / (4a^2 - 9b^2), we need to factor the numerator and the denominator.
Numerator4a^2 - 12ab + 9b^= (2a - 3b)^2
Denominator4a^2 - 9b^= (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).
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^
= (2a - 3b)^2
Denominator
4a^2 - 9b^
= (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).