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Prove that : A^-1/(A^-1+B^-1) + A^-1/(A^-1 - B^-1) = 2/(B^2 - A^2 ) - Mathematics

Sum

Prove that : `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = 2/(b^2 - a^2 )`

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Solution

`a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = 2/(b^2 - a^2 )`

L.H.S. = `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1)`

= `(1/a)/(1/a + 1/b) + (1/a)/(1/a - 1/b)`

= `(1/a)/((b + a)/(ab)) + (1/a)/((b - a)/(ab))`

= `1/a xx (ab)/(b+ a) + 1/a xx (ab)/(b - a)`

= `b/( b + a ) + b/(b - a)`

= `( b^2 - ab + b^2 + ab )/( b^2 - a^2 )`

= `( 2b^2 )/( b^2 - a^2 )`

= 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 15.1 | Page 101
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