若xyz=1,求x/(xy+x+1)+y/(yz+y+z)+z/(zx+z+1)越快越好~.

Question

若xyz=1,求 x/(xy+x+1) +y/(yz+y+z) +z/(zx+z+1)
越快越好~.

Answer 1

如果是选择题 或者是判断题最好做
令x=y=z=1 然后代入 得1
这是最简单的办法
如果是大题就这样解
x/(xy+x+1) +y/(yz+y+z) +z/(zx+z+1)
=x/(xy+x+xyz)+y/(yz+y+1)+yz/(zyx+yz+y)
=1/(y+1+yz)+y/(yz+y+1)+yz/(y+1+yz)
=(1+y+yz)/(y+1+yz)
=1