Before trying for hours, I put the expression in wolframalpha and get "no result found in terms of standard mathematical functions".

Try to express 2x-2\sqrt(x^2 - 1) as a square by observing that x^2 - 1 = (x+1)(x-1)

Before trying for hours, I put the expression in wolframalpha and get "no result found in terms of standard mathematical functions".

Try to express 2x-2\sqrt(x^2 - 1) as a square by observing that x^2 - 1 = (x+1)(x-1)