Question

已知1/x+1/y=1/6,1/y+1/z=1/9,1/z+1/x=1/15.求xyz/(xy+yz+zx)的值.

Answer 1

1/x+1/y=1/6,1/y+1/z=1/9,1/z+1/x=1/15

2(1/x+1/y+1/z)=1/6+1/9+1/15=31/90

1/x+1/y+1/z=31/180

(xy+yz+zx)/xyz=31/180

xyz/（xy+yz+zx）=180/31