What is \frac{1}{bc(a-b)(a-c)}+\frac{1}{ca(b-c)(b-a)}+\frac{1}{ab(c-a)(c-b)} equal to?

Explanation

Taking the common denominator abc(a-b)(b-c)(c-a), the numerator becomes -a(b-c) - b(c-a) - c(a-b) = -ab+ac-bc+ab-ac+bc = 0. Hence, the whole expression is 0.

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