Final answer:
The domain of the rational function f(x) = x/(x^2-4) is all real numbers except where the denominator is zero, which is at x = -2 and x = 2. Hence, the correct domain is (-∞, -2) ∪ (-2, 2) ∪ (2, ∞).
Step-by-step explanation:
To determine the domain of the rational function f(x) = \frac{x}{x^2-4}, we need to consider the values of x for which the function is defined. A rational function is undefined where its denominator is zero. For f(x), the denominator x^2 - 4 is zero when x = -2 or x = 2, as x^2 - 4 factors into (x + 2)(x - 2).
Therefore, the function is undefined at these two points. The domain of f(x) is all real numbers except x = -2 and x = 2. So, the correct domain is given by option D: (-∞, -2) ∪ (-2, 2) ∪ (2, ∞).