Since, a + b + c = 0
Then, a + b = - c .....(i)
a + c = - b ........(ii)
b + c = - a ......(iii)
Now,[(a + b)/c + (b + c)/a + (c + a)/b)] x [a/(b + c) + b/(c + a) + c/(a + b)]
Now, putting the value of a + b, b + c and c + a from Eqs (i), (ii) and (iii), we get
Given expression = [(-c)/c + (-a)/a + (-b)/b] [a/-a + b/-b + c/-c]
[(-1) + (-1) + (-1)] [(-1) + (-1) + (-1)]
= (-3) x (-3)
= 9
