simplify the expression ${\sqrt{x - 2\sqrt{x -1}} +\sqrt{x + 2\sqrt{x -1}}}$ 
Simplify the expression ${\sqrt{x - 2\sqrt{x -1}} +\sqrt{x + 2\sqrt{x -1}}}$

The problem is from a not so well renowned book for calculus in India - Concepts of Functions & Calculus - Vikas Rahi, ISBN 9780070080805. The answer for this question is given as
$$\lvert \sqrt{x-1} -1  \rvert + \lvert \sqrt{x-1}+1 \rvert$$
My efforts weren't great at all, I tried rationalizing them but the denominator becomes very similar to the question, which is totally not helpful for simplification.

Just write
\begin{eqnarray*} \sqrt{x - 2\sqrt{x -1}} +\sqrt{x + 2\sqrt{x -1}}
& = & \sqrt{x -1 - 2\sqrt{x -1} +1} +\sqrt{x -1 + 2\sqrt{x -1} +1} \\
& = & \sqrt{(\sqrt{x-1}-1)^2} + \sqrt{(\sqrt{x-1}+1)^2} \\
& = & \begin{cases} 2 & 1 \leq x\leq 2 \\ 2\sqrt{x-1} & x>2 \end{cases} 
\end{eqnarray*}
