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

Proof

\[ (a^{-1}+b^{-1})^{-1} \]

\[ = \left(\frac{1}{a} + \frac{1}{b}\right)^{-1} \]

\[ = \left(\frac{a+b}{ab}\right)^{-1} \]

\[ = \frac{ab}{a+b} \]

Hence Proved

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