xy/x+y=1 yz/y+z=2 xz/x+z=3 求xyz/x+y+z=?

xy/(x+y)=1 => (x+y)/(xy)=1 => 1/x +1/y =1
同理1/y + 1/z =1/2； 1/z+ 1/x=1/3
联立求得1/x=5/12
1/y=7/12
1/z=-1/12
所以(1/x)(1/y)+(1/y)(1/z)+(1/z)(1/x)=23/144
即：xyz/(x+y+z)=144/23