Final answer:
To simplify the given expression, recognize the difference of squares and trinomial square in the denominators, find common denominators, and subtract the fractions. The final simplified form is 2/(x - 4).
Step-by-step explanation:
The task is to simplify the expression (3x + 1)/(x² - 16) - (3x + 5)/(x² + 8x + 16). First, recognize the difference of squares in the first denominator, x² - 16 = (x + 4)(x - 4). The second expression is a trinomial square, as x² + 8x + 16 = (x + 4)².
We rewrite the expression as:
(3x + 1)/[(x + 4)(x - 4)] - (3x + 5)/(x + 4)².
To combine these fractions, they need a common denominator, which would be (x + 4)²(x - 4). By adjusting the numerators accordingly, we can subtract the fractions to find the simplified form.
After simplification, the correct option in the final answer is B. 2/(x - 4).