Question

What is the result when we simplify the expression ( 1 + 1 /x ) ( 1 − 2/x + 1 ) ( 1 + 2/ x − 1 ) ?

Answer 1

Explanation:

Let y be 1/x. Then 2y = 2/x.

We wish to simplify (1 + y)(2 - 2y)(2y).

(1 + y)(2 - 2y)(2y)

= 4y(1 + y)(1 - y)

= 4y(1 - y²)

= 4y - y³

= 4/x - 1/x³.

P.S. Writing it as (4x² - 1)/x³ is fine.