This looks ugly (but I assure you it isn't)

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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