On the problem of fraction calculation Given a + B + C = O, find the value of a (1 / B + 1 / C) + B (1 / A + 1 / C) + C (1 / B + 1 / a) There must be a process. Thank you

On the problem of fraction calculation Given a + B + C = O, find the value of a (1 / B + 1 / C) + B (1 / A + 1 / C) + C (1 / B + 1 / a) There must be a process. Thank you

It is very simple: a (1 / B + 1 / C) + B (1 / A + 1 / C) + C (1 / B + 1 / a) = a (B + C) / BC + B (a + C) / AC + C (a + b) / AB according to a + B + C = 0, B + C = - A, a + C = - B, a + B = - C, a (B + C) / BC + B (a + C) / AC + C (a + b) / AB = - (a ^ 3 + B ^ 3 + C ^ 3) / ABC = - ((a + b) (a ^ 2-AB + B ^ 2) + C ^ 3) / ABC = - (- C * (a ^ 2-AB)