已知xy/x+y=1,yz/y+z=2,xz/x+z=3求x+y+z=?

Question

已知xy/x+y=1,yz/y+z=2,xz/x+z=3求x+y+z=?

Answer 1

xy/(x+y)=1 =>xy=x+y =>1/x+1/y=1--式一 yz/(y+z)=2 =>yz=2y+2z =>1/y+1/z=1/2--式二 xz/(x+z)=3 =>xz=3x+3z =>1/x+1/z=1/3--式三 由式一、二、三 可得1/x=5/12,1/y=7/12,1/z=-1/12 即x=12/5、y=12/7、z=-12 x+y+z=-276/35.