Simplify

a(b − c) + b(c − a) + c(a − b)

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Solution

$a(b − c) + b(c − a) + c(a − b) = a \times b - a \times c + b \times c - b \times a + c \times a - c \times b = a b - a c + b c - a b + a c - b c = 0$

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\frac{a}{b + c} = \frac{b}{c + a} = \frac{c}{a + b}

a (b - c) + b (c - a) + c (a - b) = 0

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