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Prove that : ( a + B + C )/( A^-1b^-1 + B^-1c^-1 + C^-1a^-1 ) = Abc - Mathematics

Sum

Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`

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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.

Concept: Simplification of Expressions
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (C) | Q 15.2 | Page 101
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