Linear Factors Mania

Algebra Level 3

Simplify the following expression, where \(a\), \(b\) and \(c\) are distinct real numbers. \[\frac{(x-a)(x-b)}{(c-a)(c-b)}+\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-c)(x-a)}{(b-c)(b-a)}\]

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