Question

已知xyz为实数,设x/（y+z）=a,y/（z+x）=b,z/（x+y）=c

求a/(1+a)+b/(1+b)+c/(1+c)的值

Answer 1

1+a=1+x/(y+z)=(x+y+z)/(y+z)
所以a/(1+a)=[x/(y+z)]/[(x+y+z)/(y+z)]=x/(x+y+z)
同理
b/(1+b)=y/(x+y+z)
c/(1+c)=z/(x+y+z)
所以原式=(x+y+z)/(x+y+z)=1