Explanation

The symmetric choice a = b = c = 1 satisfies all three conditions and gives 1−y−z = 0, x−1+z = 0, x+y−1 = 0, whence x = y = z = 1/2. Then x/(a+x) + y/(b+y) + z/(c+z) = 3·(1/2)/(3/2) = 1. The three given relations force this value in general, so the answer is option C (1). Options 0, 3 and a+b+c already fail this symmetric test case.