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a= b+c  b= a+c  c=a+ b 

a+a= a+ b+c  =a(1+a)
b+b
= a+b+c  =b(1+b)
c+c=a+ b +c=c(1+c)

So:

 (1/1+a)+(1/1+b)+(1/1+c)=a/(a+b+c) + b/(a+b+c)+c/(a+b+c)

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

=1
 
 
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