已知x+y-z/z=x-y+z/y=-x+y+z/x,且xyz不等于0,求分式[(x+y)(x+z)(y+z)]/xyz
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已知x+y-z/z=x-y+z/y=-x+y+z/x,且xyz不等于0,求分式[(x+y)(x+z)(y+z)]/xyz的值.
(x+y-z)/z=(y+z-x)/x=(z+x-y)/y
[x+y]/z-1=[y+z]/x-1=[z+x]/y-1
[x+y]/z=[y+z]/x=[z+x]/y
设[x+y]/z=[y+z]/x=[z+x]/y=k
k[x+y+z]=[(y+z)/x]*x+[(z+x)/y]*y+[(x+y/z]*z=2[x+y+z]
k=2
(x+y)(y+z)(z+x)/xyz
=(x+y)/z*(y+z)/x*(z+x)/y=2*2*2=8
[x+y]/z-1=[y+z]/x-1=[z+x]/y-1
[x+y]/z=[y+z]/x=[z+x]/y
设[x+y]/z=[y+z]/x=[z+x]/y=k
k[x+y+z]=[(y+z)/x]*x+[(z+x)/y]*y+[(x+y/z]*z=2[x+y+z]
k=2
(x+y)(y+z)(z+x)/xyz
=(x+y)/z*(y+z)/x*(z+x)/y=2*2*2=8
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