已知1=xy/x+y,2=yz/y+z,3=xz/x+z,求x,y,z的值?

Question

已知1=xy/x+y,2=yz/y+z,3=xz/x+z,求x,y,z的值?

Answer 1

xy/x+y=1--->(x+y)/xy=1--->1/x+1/y=1 1 yz/y+z=2--->(y+z)/yz=1/2-->1/y+1/z=1/2 2 zx/z+x=3--->(z+x)/zx=1/3-->1/z+1/x=1/3 3 1/x+1/y+1/z=11/12 4 4-2 1/x=5/12 4-3 1/y=7/12 4-1 1/z=-1/12 x=12/5.y=12/7,z=-12 x+y+z=-276/35