已知xyz=1,求x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)的值已知xyz=1,求1/(xy+x+1)+1/(yz+y+1)+1/(xz+z+1)的值

Question

已知xyz=1,求x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)的值
已知xyz=1,求1/(xy+x+1)+1/(yz+y+1)+1/(xz+z+1)的值

Answer 1

解
由已知条件
xyz=1
可推出
z=1/xy
xz=1/y
yz=1/x
则原式=x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)
=x/(xy+x+1)+y/(1/x+y+1)+(1/xy)/(1/y+1/xy+1)
=x/(xy+x+1)+xy/(xy+x+1)+1/(xy+x+1)
=(xy+x+1)/(xy+x+1)
=1
好了,完成了