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Question
Prove that:
`(a^-1+b^-1)^-1=(ab)/(a+b)`
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Solution
Consider the left hand side:
`(a^-1+b^-1)^-1`
`=1/(a^-1+b^-1)`
`=1/(1/a+1/b)`
`=1/((b+a)/(ab))`
`=(ab)/(a+b)`
Therefore left hand side is equal to the right hand side. Hence proved.
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