Question

Prove that : a‐¹/ ( a‐¹ + b‐¹ ) + a‐¹/ ( a‐¹ + b‐¹ ) = 2b² /b²– a²​

Answer 1

a-¹/(a-¹ + b-¹ ) + a-¹/( a-¹ - b-¹) = 2b²/( b² - a²)

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

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

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

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

= b{ 1/( b + a) + 1/( b -a) }

= b{ 2b/( b² - a²) }

= 2b²/( b² - a²) = RHS

Hence, proved...

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Answer 2

Answer:

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