x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3=0,且1/x+1/y+1/z≠0,求x+y+z的值.

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x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3=0,且1/x+1/y+1/z≠0,求x+y+z的值.

x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3=0,且1/x+1/y+1/z≠0,求x+y+z的值.
x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3=0,且1/x+1/y+1/z≠0,求x+y+z的值.

x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3=0,且1/x+1/y+1/z≠0,求x+y+z的值.
∵x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3=0,
∴x/y+x/z+y/x+y/z+z/x+z/y+3=0
∴(x/x+y/x+z/x)+(x/y+y/y+z/y)+(x/z+y/z+z/z)=0
∴x+y+z(1/x+1/y+1/z)=0
∵1/x+1/y+1/z不等于0,
∴x+y+z=0