What A Mess

Algebra Level 3

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

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

\[\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+\frac{x}{z}+\frac{z}{y}+\frac{y}{x}\]

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