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Algebra Level 3

a+b+c=31a+1b+1c=5\begin{aligned} a + b + c = 3 \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 5 \end{aligned}

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

ab+ac+ba+bc+ca+cb.\frac{a}{b} + \frac{a}{c} + \frac{b}{a} + \frac{b}{c} + \frac{c}{a} + \frac{c}{b}.

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