\(\displaystyle \frac{1-(\sqrt{x+1})}{1+(\sqrt{x-1})}\)

Now I had thought that the method to solve it was to just multiply the numerator and denominator by the conjugate of the denominator, but I keep getting answers that are different from the solution provided, which is:

\(\displaystyle \frac{(2(\sqrt{x+1})-x-2)}{x}\)

Here is what I am trying to do and how I am getting stuck:

\(\displaystyle \frac{(1-\sqrt{x+1})}{1+\sqrt{x-1})} = \frac{(1-\sqrt{x+1})}{1+\sqrt{x-1})} * \frac{1-\sqrt{x-1})}{1-\sqrt{x-1})} = \frac{(1-\sqrt{x-1} - \sqrt{x+1} + \sqrt{(x+1)(x-1)})}{(1-x+1)}\)

This is where I get stuck or realize I am probably doing something totally wrong.