Explanation

Put a = x−y, b = y−z, c = z−x; then a + b + c = 0. The identity a³ + b³ + c³ = 3abc holds whenever a+b+c = 0, so the numerator is 3(x−y)(y−z)(z−x). Dividing by 9(x−y)(y−z)(z−x) gives 3/9 = 1/3. The answer is (B).