To simplify this expression, we first factor the numerator:

4n² + 7n - 2 = (4n - 1)(n + 2)

Now, we divide the numerator by the denominator:

[(4n - 1)(n + 2)] / (1 - 16n²)

We can further factor the denominator as a different of squares:

(1 - 16n²) = (1 - 4n)(1 + 4n)

Now, we rewrite the division expression:

[(4n - 1)(n + 2)] / [(1 - 4n)(1 + 4n)]

Next, we simplify and cancel out common factors from the numerator and denominator:

= (4n - 1) / (1 + 4n)

Therefore, the simplified expression is:

(4n - 1) / (1 + 4n)