Question
Fri March 23, 2012 By:

. IF a= x/x+z , b = y/z+x, c= z/x+y. Then Prove that 1-a/1+a + b/1+b + c/1+c = 1. Its conditional identities problem

Expert Reply
Fri March 23, 2012

 x/(y+z)=a      1 + a = (x + y + z)/(y + z)        a/(1+a) = x/(x+y+z)

y/(z+x)=b      1 + b = (x + y + z)/(z+x)        b/(1+b) = y/(x+y+z)

z/(x+y)=c      1 + c = (x + y + z)/(x+y)        c/(1+c) = z/(x+y+z)

Hence, a/1+a + b/1+b + c/1+c = 1
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