Question

Prove that a⁻¹/(a⁻¹ + b⁻¹) + a⁻¹/(a⁻¹ – b⁻¹) = 2b²/(b² – a²)

Answer 1

Prove

=a⁻¹/(a⁻¹ + b⁻¹) + a⁻¹/(a⁻¹ – b⁻¹)

= 2b²/(b² – a²)

=>1/a+1/a

=>1/a+1/b 1/a-1/b

=>1/a×ab/b+a + 1/a×ab/b-a

=>b/b+a + b/b-a

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

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

=>b²-ab/b²-a² + b²+ ab/b²-a²

=>b²-ab+b² +b²+ab/b²-a²

=>2b²/b²-a²