Let x, y, z be variables such that (x+y+z)=k, where k is a constant. If (x+z-y)\times(x-z+y) is proportional to yz, then (y+z-x) is proportional to:

Explanation

Let x+y+z=k. The given product is (k-2y)(k-2z) = k^2 - 2k(y+z) + 4yz. For this expression to be proportional to yz for all variables, we must have k=0. If k=0, x+y+z=0 \implies y+z-x = -x-x = -2x, which is proportional to x.

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