To simplify the expression:

(49a^2 - 16b^2)(b+1) / (4b - 7ab + 4b^2 - 7a)

First, factorize the numerator and the denominator:

Numerator: (49a^2 - 16b^2)(b+1) = (7a + 4b)(7a - 4b)(b+1)

Denominator: 4b - 7ab + 4b^2 - 7a = 4b(1 + b) - 7a(1 + b) = (4b - 7a)(1 + b)

Now, simplify the expression:

[(7a + 4b)(7a - 4b)(b+1)] / [(4b - 7a)(1 + b)]

= [(7a + 4b)(7a - 4b)] / [(4b - 7a)]

= [49a^2 - 16b^2] / [4b - 7a]

Therefore, the simplified expression is (49a^2 - 16b^2) / (4b - 7a).