$\quad A =\sqrt{x^2 + 2\sqrt{x^2 -1}} - \sqrt{x^2 - 2\sqrt{x^2 -1}}$
$ĐKXĐ: x^2 - 1 \geqslant 0\Leftrightarrow \left[\begin{array}{l}x\geqslant 1\\x \leqslant -1\end{array}\right.$
Ta có:
$\quad A = \sqrt{x^2-1 + 2\sqrt{x^2 -1}+1} - \sqrt{x^2-1 - 2\sqrt{x^2 -1}+1}$
$\to A = \sqrt{\left(\sqrt{x^2-1} +1\right)^2} - \sqrt{\left(\sqrt{x^2-1} -1\right)^2}$
$\to A =\left|\sqrt{x^2 -1} +1\right| - \left|\sqrt{x^2 -1} -1\right|$
$\to A = \sqrt{x^2 -1} +1- \left|\sqrt{x^2 -1} -1\right|$
$+)\quad TH1:\ \left[\begin{array}{l}x\geqslant \sqrt2\\x \leqslant -\sqrt2\end{array}\right.$
$\to A = \sqrt{x^2 -1} +1 - \left(\sqrt{x^2 -1} -1\right)$
$\to A = 2$
$+)\quad TH2:\ \left[\begin{array}{l}1 \leqslant x\leqslant \sqrt2\\ -\sqrt2\leqslant x \leqslant -1\end{array}\right.$
$\to A = \sqrt{x^2 -1} +1 - \left(1 - \sqrt{x^2 -1}\right)$
$\to A = 2\sqrt{x^2 -1}$
