Hi,

Does anyone know straightforward steps to make the following simplification:

$\displaystyle (x+\sqrt{x^2-1})^2-(x+\sqrt{x^2-1})^{-2}=4x\sqrt{x^2-1}$

I've tried to make the step:

$\displaystyle =\frac{(x+\sqrt{x^2-1})^4-1}{(x+\sqrt{x^2-1})^{2}}$

and multiplying out etc, with the aim of the simplified expression as a factor in the nominator, but then just get into a mess. I'd really like to understand how to spot when such a simplification would be possible.

Many thanks,

Chris