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Algebra Level 5

For real numbers \(A, a, b,\) and \(c\), minimize

\(\frac { (A-a)(A-b) }{ (c-a)(c-b) } +\frac { (A-a)(A-c) }{ (b-a)(b-c) } +\frac { (A-b)(A-c) }{ (a-b)(a-c) } \)

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