Let a, b, c be real number such that a + b + c = 5 and 1/(b + c) + 1/(c + a) + 1/(a + b) = 6. Find a/(b + c) + b/(c + a) + c/(a + b).
a + b + c = 5. (1)
Divide (1) by b + c: a/(b+c) + 1 = 5/(b+c). (2)
Divide (1) by a + c: b/(a+c) + 1 = 5/(a+c). (3)
Divide (1) by a + b: c/(a+b) + 1 = 5/(a+b). (4)
Add (2), (3) and (4): a/(b+c) + b/(a+c) + c/(a+b) + 3 = 5*6
Hence a/(b+c) + b/(a+c) + c/(a+b) = 27
