Let's simplify this expression step by step.

First step: Factor the numerator

6a^2 + 19a - 1 = (3a - 1)(2a + 1)

Second step: Factor the denominator (as a difference of squares)

1 - 25a^2 = (1 - 5a)(1 + 5a)

Now, simplify the expression:

(3a - 1)(2a + 1) / (1 - 5a)(1 + 5a)

= (3a - 1)(2a + 1) / [(1 - 5a)(1 + 5a)]

= [(3a - 1)(2a + 1)] / [(1 - 5a)(1 + 5a)]

Therefore, the simplified expression is [(3a - 1)(2a + 1)] / [(1 - 5a)(1 + 5a)].