x+y+z=6 ··· Ex.1, xy+yz+zx=11 ··· Ex.2, xyz=6 ··· Ex.3
Square LHS of Ex.1. We have: (x+y+z)²=x²+y²+z²+2(xy+yz+zx) ··· Ex.4
Plug Ex.1 and Ex.2 into Ex.4. We have: 6²=x²+y²+z²+2·(11) That is: x²+y²+z²=14 ··· Ex.5
Divide Ex.5 by Ex.3. We have: (x²+y²+z²)/xyz=14/6, so x²/xyz + y²/xyz + z²/xyz=14/6
Reduce the fractions in both sides. We have: x/yz + y/zx + z/xy= 7/3
The answer is: C=7/3