Question

If `a + b + c = 2015` and `1/(a+b) + 1/(b+c) + 1/(c+a) = 1/65`, what is `c/(a+b) + b/(c+a) + a/(b+c)` ?

Thanks in advance for the answer.

Answer 1

`28`

Explanation:

Making

`(1/(a + b) + 1/(b + c) + 1/(c + a))(a+b+c)=2015/65=31` or

#a/(a + b) + b/(a + b) + c/(a + b) + a/(a + c) + b/(a + c) + c/( a + c) + a/(b + c) + b/(b + c) + c/(b + c) = 31# we have

`c/(a+b) + b/(c+a) + a/(b+c) = 28`