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Algebra Level 2

Let \(x\), \(y\), and \(z\) be real numbers such that \( x+y+z=6\) and \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=2 \). Find the value of \(\dfrac{(x+y)}{z}+\dfrac{(y+z)}{x}+\dfrac{(x+z)}{y}\).

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