I need to demonstrate that

Question

If x>2 then 1 < 1

√2-2 x - 2

Answer 1

For x>2, 1/(x-2) is > 0 and 1/[sqrt(2)-2] is always negative.

However, I am not sure that you submitted the question correctly.

Answer 2

Since x > 2 both denominators are greater than zero.

x - 2 < √2 - 2

x < √2

Contradictory! The posit is false.