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

Note x + z − y = k − 2y and x + y − z = k − 2z (where x − z + y = x + y − z). Their product = (k − 2y)(k − 2z). This is proportional to yz. We need to find what (y + z − x) = k − 2x is proportional to. By symmetry of the relation, since the product of two of the (k − 2·variable) terms is proportional to the product of the other two variables, the third term (k − 2x) must be proportional to x.