xy/x+y=1,yz/y+z=2,xz/x+z=3,求x的值

Question

xy/x+y=1,yz/y+z=2,xz/x+z=3,求x的值

Answer 1

将三式都取倒数得到：
1/x+1/y = 1 (1)
1/y+1/z = 1/2 (2)
1/x+1/z = 1/3 (3)
(3)-(2) 得到
1/x-1/y = -1/6 (4)
(1)+(4) 得到
2/x=5/6
所以 x = 12/5 =2.4