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# Hard Algebra Problem

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Can somebody please tell me how to do this problem? I'm stuck and I don't know how to begin.

If $$abc=13 and \left(a+\frac{1}{b}\right)\left(b+\frac{1}{c}\right)\left(c+\frac{1}{a}\right)=\left(1+\frac{1}{a}\right)\left(1+\frac{1}{b}\right)\left(1+\frac{1}{c}\right),find a+b+c.$$

Jun 3, 2020