# Find The Value of [(a + b)/c + (b + c)/a + (c + a)/b] [a/(b + c) + b/(c + a) + c/(a + b)] : If

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If a + b + c = 0, then the value of [(a + b)/c + (b + c)/a + (c + a)/b] [a/(b + c) + b/(c + a) + c/(a + b)] is

- 9
- 0
- 8
- -3

Best answer

**Answer: (1) 9
Explanation:-
** Given-

a + b + c = 0

Then, a + b = – c ……………………. (1)

a + c = – b …………………………… (2)

b + c = -a ………………………………. (3)

Now,

[(a + b)/c + (b + c)/a + (c + a)/b] [a/(b + c) + b/(c + a) + c/(a + b)]

Put the value of a + b, b + c, c + a from equation (1), (2) & (3)

=[(-c)/c + (-a)/a + (-b)/b] = [a/(-a) + b/(-b) + c/(-c)]

=[(-1) + (-1) + (-1)] [(-1) + (-1) + (-1) ]

=(- 1 – 1 – 1) (-1 – 1 – 1)

= (-3) (-3)

= 9

Hence, the answer is (1) 9.