x分之y+z=y分之z+x=z分之x+y(x+y+z不等于0),求x+y+z分之x+y-z
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x分之y+z=y分之z+x=z分之x+y(x+y+z不等于0),求x+y+z分之x+y-z
令(y+z)/x=(z+x)/y=(x+y)/z=k
y+z=kx
x+z=ky
x+y=kz
2(x+y+z)=k(x+y+z)
2(x+y+z)=k(x+y+z)
(2-k)(x+y+z)=0(x+y+z≠ 0)
k=2
x+y=2z
(x+y-z)/(x+y+z)
=(2z-z)/(2z+z)
=z/3z
=1/3
y+z=kx
x+z=ky
x+y=kz
2(x+y+z)=k(x+y+z)
2(x+y+z)=k(x+y+z)
(2-k)(x+y+z)=0(x+y+z≠ 0)
k=2
x+y=2z
(x+y-z)/(x+y+z)
=(2z-z)/(2z+z)
=z/3z
=1/3
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