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\frac{a^{2} - ab - ac + bc}{a^{2} + ab - ac - bc} = \frac{a (a - b) - c (a - b)}{a (a + b) - c (a + b)} = \frac{(a - b) (a - c)}{(a + b) (a - c)} = \frac{a - b}{a + b} So, \frac{a^{2} - ab - ac + bc}{a^{2} + ab - ac - bc} = \frac{a - b}{a + b}

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