奥数题123a+b+c=0 a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)= （化简）

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+b)/c+(b+c)/a+(a+c)/b
= -c/c+(-a)/a+(-b)/b
= -3