We know that, a 3 - b 3 = (a - b) (a 2 + a × b + b 2 ) Using this formula, we get = a 3 - 1/a 3 – 2 (a – 1/a) = (a – 1/a) (a 2 + a × 1/a + 1/a 2 ) – 2 (a – 1/a) = (a – 1/a) (a 2 + 1 + 1/a 2 – 2) =

Factorize:

We know that,

a³ - b³ = (a - b) (a² + a × b + b²)

Using this formula, we get

= a³ - 1/a³ – 2 (a – 1/a)

= (a – 1/a) (a² + a × 1/a + 1/a²) – 2 (a – 1/a)

= (a – 1/a) (a² + 1 + 1/a² – 2)