58问答库 > 已知xyz=1求(x⼀xy+x+1)+(y⼀yz+y+1)+(z⼀zx+z+1)的值

已知xyz=1求(x⼀xy+x+1)+(y⼀yz+y+1)+(z⼀zx+z+1)的值

2025-05-17 18:20:08

推荐回答（2个）

回答（1）：

解:xyz=1
x/(xy+x+1)+y/(yz+y+1)+z/(zx+z+1)将x/(xy+x+1)中的1换为xyz得:
=x/(xy+x+xyz)+y/(yz+y+1)+z/(zx+z+1)
=1/(yz+y+1)+y/(yz+y+1)+z/(zx+z+1)
=(1+y)/(yz+y+1)+z/(zx+z+1)将(1+y)/(yz+y+1)中的1换为xyz得:
=(xyz+y)/(yz+y+xyz)+z/(zx+z+1)
=(xz+1)/(zx+z+1)+z/(zx+z+1)
=(zx+z+1)/(zx+z+1)
=1

回答（2）：