Let \(x, y, z\) be positive numbers such that:

\((1)\) \(x = \frac{a}{a+b}\)

\((2)\) \(y = \frac{b}{b+c}\)

\((3)\) \(z = \frac{c}{c+a}\)

Prove the following:

\(x+y+z > 1\)

Let \(x, y, z\) be positive numbers such that:

\((1)\) \(x = \frac{a}{a+b}\)

\((2)\) \(y = \frac{b}{b+c}\)

\((3)\) \(z = \frac{c}{c+a}\)

Prove the following:

\(x+y+z > 1\)

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TopNewestHint: fund \(\frac{1}{x}\) and similar, apply AM-HM on \(x,y,z\), and then try to simplify

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