Prove: \(\frac{a+b+c}{a^{-1}+b^{-1}+c^{-1}} = abc\)

Proof

\[ = \frac{a+b+c}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}} \]

\[ = \frac{a+b+c}{\frac{bc+ca+ab}{abc}} \]

\[ = (a+b+c)\cdot \frac{abc}{ab+bc+ca} \]

\[ = abc \]

Hence Proved

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