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Question
Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`
Solution
L.H.S. = `( 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 )( abc ))/( a + b + c )`
= abc
= R.H.S.
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