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My first post was an observation rather than a proof.
All three LHS terms in the first equation are quadratics in x.
Evaluate both LHS expressions at x = a, x = b, x = c
In each case, two of the quotients go to zero and the third to one.
In each case, two of the quotients go to zero and the third to one.In the first equation, two of the terms (which are the coefficients of a, b, and c in the second) go to zero and the third to one.
Not true.
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