Question

x.y.z三个数满足xy/x+y=-2.yz/y+z=4/3,zx/z+x=负的4/3求xyz/xy+xz+yz

Answer 1

xy/(x+y)=-2==>(x+y)/xy=-1/2

1/x+1/y=-1/2

同理：

1/y+1/x=3/4

1/z+1/x= - 3/4

三式相加得：

2(1/x+1/y+1/z）=-1/2

2(xy+yz+zx)/xyz= - 1/2

(xy+yz+zx)/xyz= - 1/4