设XYZ=1,求X/(XY+X+1)+Y/(YZ+y+1)+Z/(ZX+Z+1)的值

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设XYZ=1,求X/(XY+X+1)+Y/(YZ+y+1)+Z/(ZX+Z+1)的值
设XYZ=1,求X/(XY+X+1)+Y/(YZ+y+1)+Z/(ZX+Z+1)的值

设XYZ=1,求X/(XY+X+1)+Y/(YZ+y+1)+Z/(ZX+Z+1)的值
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