Ta có: \(\sqrt{\frac{a+x^2}{x}-2\sqrt{a}}-\sqrt{\frac{a+x^2}{x}+2\sqrt{a}}\)
\(=\frac{\sqrt{a+x^2-2x\sqrt{a}}-\sqrt{a+x^2+2\cdot x\cdot\sqrt{a}}}{\sqrt{x}}\)
\(=\frac{\sqrt{\left(x-\sqrt{a}\right)^2}-\sqrt{\left(x+\sqrt{a}\right)^2}}{\sqrt{x}}\)
\(=\frac{\left|x-\sqrt{a}\right|-\left|x+\sqrt{a}\right|}{\sqrt{x}}\)
\(=\frac{\left|x-\sqrt{a}\right|-x-\sqrt{a}}{\sqrt{x}}\)
\(=\left[{}\begin{matrix}\frac{x-\sqrt{a}-x-\sqrt{a}}{\sqrt{x}}\left(x\ge\sqrt{a}\right)\\\frac{\sqrt{a}-x-x-\sqrt{a}}{\sqrt{x}}\left(x< \sqrt{a}\right)\end{matrix}\right.\)
\(=\left[{}\begin{matrix}-\frac{2\sqrt{a}}{\sqrt{x}}\\-2\sqrt{x}\end{matrix}\right.\)
