Explanation

Given:

x = 1 / (√2 - 1)

To simplify, multiply the numerator and denominator by (√2 + 1):

x = 1 / (√2 - 1) × (√2 + 1) / (√2 + 1)

= (√2 + 1) / (√2² - 1²)

= (√2 + 1) / (2 - 1)

= (√2 + 1)

Now, find x - 1/x:

x - 1/x = (√2 + 1) - 1 / (√2 + 1)

= (√2 + 1) - (√2 - 1) / (√2 + 1)(√2 - 1)

= (√2 + 1) - (√2 - 1) / (2 - 1)

= (√2 + 1) - (√2 - 1)

= (√2 + 1 - √2 + 1)

= 2