\frac{AO}{DO} \cdot \frac{BO}{EO} \cdot \frac{CO}{FO}=\left(x+{1 \over z} \Bigg) \Bigg(y+\frac{1}{x} \right) \left(\frac{1}{y}+z \right)=\frac{(xz+1)(xy+1)(yz+1)}{xyz}