已知xy/(x+y)=1,yz/(y+z)=2,zx/(z+x)=3,求x的值

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已知xy/(x+y)=1,yz/(y+z)=2,zx/(z+x)=3,求x的值
已知xy/(x+y)=1,yz/(y+z)=2,zx/(z+x)=3,求x的值

已知xy/(x+y)=1,yz/(y+z)=2,zx/(z+x)=3,求x的值
取倒数,得:
(1/x)+(1/y)=1
(1/y)+(1/z)=1/2
(1/z)+(1/x)=1/3
三个式子相加,得:(1/x)+(1/y)+(1/z)=11/12
此式子与第二个式子相减,得:1/x=5/12,得:x=12/5

x=12/5
y=12/7
z=-12

xy/(x+y)=1 (x+y)/xy=1 1/x+1/y=1 (4)
yz/(y+z)=2 (y+z)/yz=1/2 1/y+1/z=1/2 (5)
zx/(x+z)=3 (x+z)/xz=1/3 1/x+1/z=1/3 (6)
(4)+(6)-(5)得
2/x=1+1/3-1/2
2/x=5/6
x=12/5