p=(x y)^2/xy z

\[\begin{array}{l}P = \frac{{{{\left( {x + y} \right)}^2}}}{{xy + z}}.\frac{{{{\left( {y + z} \right)}^2}}}{{yz + x}}.\frac{{{{\left( {z + x} \right)}^2}}}{{z{\rm{x}} + y}}\\P = \frac{{{{\left( {x + y} \right)}^2}}}{{xy + 1 - x - y}}.\frac{{{{\left( {y + z} \right)}^2}}}{{yz + 1 - y - z}}.\frac{{{{\left( {z + x} \right)}^2}}}{{z{\rm{x}} + 1 - z - x}}\\P = \frac{{{{\left( {x + y} \right)}^2}}}{{\left( {x - 1} \right)\left( {y - 1} \right)}}.\frac{{{{\left( {y + z} \right)}^2}}}{{\left( {y - 1} \right)z - 1}}.\frac{{{{\left( {z + x} \right)}^2}}}{{\left( {z - 1} \right)\left( {x - 1} \right)}}\\P = \frac{{{{\left( {1 - z} \right)}^2}}}{{\left( {x - 1} \right)\left( {y - 1} \right)}}.\frac{{{{\left( {1 - x} \right)}^2}}}{{\left( {y - 1} \right)z - 1}}.\frac{{{{\left( {1 - y} \right)}^2}}}{{\left( {z - 1} \right)\left( {x - 1} \right)}}\\P = 1\end{array}\]