x,y,z为实数,且x+y+z≠0,设x/(y+z)=a,y/(z+x)=b,z/(x+y)=c则a/(1+a)+b/(1+b)+c/(1+c)=?

Question

x,y,z为实数,且x+y+z≠0,设x/(y+z)=a,y/(z+x)=b,z/(x+y)=c
则a/(1+a)+b/(1+b)+c/(1+c)=?

Answer 1

a/(1+a) = [x/(y+z)] / [1+x/(y+z)]
= x/(x+y+z)
同理可得其余
a/(1+a)+b/(1+b)+c/(1+c) = x/(x+y+z)+y/(x+y+z)+z/(x+y+z)
= (x+y+z)/(x+y+z)
= 1