Упростите выражение:

\frac{a^{2} - 4 a c + 3 b c}{a^{2} - a b + b c - a c} + \frac{a + 3 b}{b - a} + \frac{a + 2 c}{a - c}

Упростите выражение: a 2 − 4 a c + 3 b c a 2 − a b + b c − a c + a + 3 b b − a + a + 2 c a − c .

\frac{a^{2} - 4 a c + 3 b c}{a^{2} - a b + b c - a c} + \frac{a + 3 b}{b - a} + \frac{a + 2 c}{a - c} = \frac{a^{2} - 4 a c + 3 b c - (a^{2} + 3 a b - a c - 3 b c) + a^{2} + 2 a c - a b - 2 b c}{(a - b) (a - c)} = \frac{a^{2} - a c - 4 b c - 4 a b}{(a - b) (a - c)} = \frac{a (a - c) - 4 b (a - c)}{(a - b) (a - c)} = \frac{(a - 4 b) (a - c)}{(a - b) (a - c)} = \frac{a - 4 b}{a - b}