Given that a, B, C are unequal real numbers, and X / A-B = Y / B-C = Z / C-A, find the value of X + y + Z

Let X / (a-b) = Y / (B-C) = Z / (C-A) = K
So x = (a-b) k, y = (B-C) k, z = (C-A) K
So x + y + Z = (a-b) K + (B-C) K + (C-A) k
=(A-B+B-C+C-A)k
=0 ×k
=0

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