Question

  Упростите выражение

     1______ + __2_________  +  __1_______
a²-ac-ab+bc    b²-ab-bc+ac        c²-ac-bc+ab

Answer 1

1/(a²-ac-ab+bc) + 2/( b²-ab-bc+ac) + 1/(c²-ac-bc+ab) = 1/(a(a-c) + b(c-a)) + 2/(b(b-a) + c(a-b)) + 1/(c(c-a) + b(a-c)) = 1/(a-b)(a-c) + 2/(a-b)(c-b) + 1/(a-c)(b-c) = 1/(a-b)(a-c) + 2/(a-b)(c-b) - 1/(a-c)(c-b) = ((c-b) + 2(a-c) - (a-b))/(a-b)(a-c)(c-b) = (c-b + 2a - 2c - a + b)/(a-b)(a-c)(c-b) = (a-c)/(a-b)(a-c)(c-b) = 1/(a-b)(c-b)