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