a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)
=a/b+a/c+b/a+b/c+c/a+c/b
=(b+c)/a+(c+a)/b+(a+b)/c
∵a+b+c=0
→a+b=-c,c+a=-b,b+c=-a
∴原式=-1-1-1=-3
a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)
=a/b+a/c+b/a+b/c+c/a+c/b
=(b+c)/a+(c+a)/b+(a+b)/c
∵a+b+c=0
→a+b=-c,c+a=-b,b+c=-a
∴原式=-1-1-1=-3