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

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

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

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

x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)
=x/(xy+x+xyz)+y/(yz+y+1)+yz/(xyz+yz+y)
=1/(y+yz+1)+y/(yz+y+1)+yz/(y+yz+1)
=(1+yz+y)/(y+yz+1)
=1

答案是 1
最笨的办法是通分去解。。。。
最快的办法是带入特殊值,嘿嘿。。。
寻求好的解题方法最好给定你现在学哪本书还有是否需要详细步骤啊等。这样大家也有思路,有重点的回答啊。。。

=x/(xy+x+xyz)+y/(yz+y+1)+yz(xyz+yz+y)
=1/(y+1+yz)+y/(yz+y+1)+yz/(1+y+yz)
=(1+yyz)/(1+y+yz)
=1