Simplify

a(b − c) − b(c − a) − c(a − b)

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Solution

$a (b - c) - b (c - a) - c (a - b) = a \times b - a \times c - b \times c + b \times a - c \times a + c \times b = ab + ab - ac - ac - bc + bc = 2 ab - 2 ac = 2 a (b - c)$

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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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