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Algebra Level 3

\[\begin{align*} a + b + c = 3 \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 5 \end{align*}\]

If \(a,b,c\) are nonzero real numbers satisfying the above equations, find the value of

\[\frac{a}{b} + \frac{a}{c} + \frac{b}{a} + \frac{b}{c} + \frac{c}{a} + \frac{c}{b}.\]

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