If f(x) = (x+2)/(x−2) and g(x) = (x−2)/(x+2), what is the correct form of (f+g)(x)?

Correct answer: (2x²+8)/(x²−4), x ≠ ±2

To add rational functions, use a common denominator rather than adding numerators directly. The denominators are x−2 and x+2, so their common denominator is (x−2)(x+2) = x²−4. Thus (f+g)(x) = [(x+2)² + (x−2)²]/[(x−2)(x+2)]. Expanding gives (x²+4x+4) + (x²−4x+4) = 2x²+8; the middle terms cancel. Hence the result is (2x²+8)/(x²−4). The original functions are undefined at x = 2 and x = −2, so these values must remain excluded even if later cancellation were possible. Option A is correct. Option B omits the square terms, C omits a factor of 2, and D incorrectly treats the reciprocal expressions as exact additive inverses.