What A Mess

Algebra Level 3

{x+y+z=261x+1y+1z=31 \begin{cases}{x+y+z=26} \\ {\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=31}\end{cases}

The two equations above satisfy the real numbers x,y,zx,y,z. What is the value of the expression below?

xy+yz+zx+xz+zy+yx\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+\frac{x}{z}+\frac{z}{y}+\frac{y}{x}

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