x/y+z=a,y/z+x=b,z/x+y=c,x+y+z不等于0,求a/1+a+b/1+b+c/1+c

题目

x/y+z=a,y/z+x=b,z/x+y=c,x+y+z不等于0,求a/1+a+b/1+b+c/1+c

答案

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