(y+z)/x=(z+x)/y=(x+y)/z求x+y-z/x+y+z的值

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(y+z)/x=(z+x)/y=(x+y)/z求x+y-z/x+y+z的值
(y+z)/x=(z+x)/y=(x+y)/z求x+y-z/x+y+z的值

(y+z)/x=(z+x)/y=(x+y)/z求x+y-z/x+y+z的值
令(y+z)/x=(z+x)/y=(x+y)/z=k
则y+z=xk
z+x=yk
x+y=zk
三式相加得2(x+y+z)=k(x+y+z)
k=2
∴由x+y=2z
得x+y-z=z
而x+y+z=2z+z=3z
所以(x+y-z)/(x+y+z)
=z/(3z)
=1/3

设
(y+z)/x=(z+x)/y=(x+y)/z=t
根据合比定理
t=(y+z+z+x+x+y)/(x+y+z)=2
所以(x+y)/z=2
x+y=2z
所以
x+y-z/x+y+z=(2z-z)/(2z+z)=1/3

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