急用,等答案.若xyz=1,求 (x/xy+x+1)+(y/yz+y+1)+(z/xz+z+1) 的值
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急用,等答案.若xyz=1,求 (x/xy+x+1)+(y/yz+y+1)+(z/xz+z+1) 的值
![急用,等答案.若xyz=1,求 (x/xy+x+1)+(y/yz+y+1)+(z/xz+z+1) 的值](/uploads/image/z/11520700-52-0.jpg?t=%E6%80%A5%E7%94%A8%2C%E7%AD%89%E7%AD%94%E6%A1%88.%E8%8B%A5xyz%3D1%2C%E6%B1%82+%28x%2Fxy%2Bx%2B1%29%2B%28y%2Fyz%2By%2B1%29%2B%28z%2Fxz%2Bz%2B1%29+%E7%9A%84%E5%80%BC)
xyz=1
所以x=1/yz
xy=1/z
xz=1/y
所以原式=
(1/yz)/(1/z+1/yz+1)+y/(yz+y+1)+z/(1/y+z+1)
第一个式子上下乘yz
第三个式子上下乘y
=1/(yz+y+1)+y/(yz+y+1)+yz/(yz+y+1)
=(yz+y+1)/(yz+y+1)
=1
所以x=1/yz
xy=1/z
xz=1/y
所以原式=
(1/yz)/(1/z+1/yz+1)+y/(yz+y+1)+z/(1/y+z+1)
第一个式子上下乘yz
第三个式子上下乘y
=1/(yz+y+1)+y/(yz+y+1)+yz/(yz+y+1)
=(yz+y+1)/(yz+y+1)
=1
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