Final answer:
The least common denominator of the given fractions is (x+2)(x-1)(x+4)(x-4).
Step-by-step explanation:
To find the least common denominator of the fractions 3/(x^2-x-2) and -2/(x^2-16), we need to factor the denominators and identify the common factors. The first denominator can be factored as (x+2)(x-1), and the second denominator can be factored as (x+4)(x-4). The common factors are (x+2) and (x-1), so the least common denominator is (x+2)(x-1)(x+4)(x-4), which corresponds to option A.