A Simplification Problem

Simplify

$$\frac{(x-a)(x-b)}{(c-a)(x-b)} + \frac{(x-b)(x-c)}{(a-b)(a-c)} + \frac{(x-a)(x-c)}{(b-a)(b-c)}$$

where a, b and c are three distinct numbers.

Source: Quantum, Jul/Aug 1996, p. 29