a+b+c=0 abc不等于0 求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值
问题描述：
a+b+c=0 abc不等于0 求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值
答
解:a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)
=a/b+a/c+b/c+b/a+c/a+c/b
=(a+c)/b+(b+c)/a+(a+b)/c
=-c/c-a/a-b/b=-3