Question

已知三个数x,y,z,满足xy/x+y=-2。yz/y+4=4/3,zx/z+x=-4/3,则xyz/xy+xz+yz=?

Answer 1

xy/(x+y)=-2 (x+y)/(xy)=-1/2, 1/x +1/y =-1/2
yz/(y+z)=4/3, (y+z)/(yz)=3/4, 1/y +1/z =3/4
zx/(z+x)=-4/3, (z+x)/(zx)=-3/4 1/z +1/x=-3/4
将以上三式相加，得：
2(1/x+1/y+1/z)
=-1/2+3/4-3/4(1/x+1/y+1/z)
=-1/4
所以：(xyz)/(xy+yz+zx)
=1/[(xy+yz+zx)/xyz]
=1/(xy/xyz+yz/xyz+zx/xyz)
=1/(1/x+1/y+1/z)
=1/(-1/4)
=-4