Ta có: \(\dfrac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}-\dfrac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
\(=\dfrac{6+2\sqrt{5}}{2\sqrt{2}+\sqrt{2}\cdot\left(\sqrt{5}+1\right)}-\dfrac{6-2\sqrt{5}}{2\sqrt{2}-\sqrt{2}\left(\sqrt{5}-1\right)}\)
\(=\dfrac{6+2\sqrt{5}}{2\sqrt{2}+\sqrt{10}+\sqrt{2}}-\dfrac{6-2\sqrt{5}}{2\sqrt{2}-\sqrt{10}+\sqrt{2}}\)
\(=\dfrac{6+2\sqrt{5}}{3\sqrt{2}+\sqrt{10}}-\dfrac{6-2\sqrt{5}}{3\sqrt{2}-\sqrt{10}}\)
\(=\dfrac{\left(6+2\sqrt{5}\right)\left(3\sqrt{2}-\sqrt{10}\right)-\left(6-2\sqrt{5}\right)\left(3\sqrt{2}+\sqrt{10}\right)}{8}\)
\(=\dfrac{18\sqrt{2}-6\sqrt{10}+6\sqrt{10}-10\sqrt{2}-18\sqrt{2}-6\sqrt{10}+6\sqrt{10}+10\sqrt{2}}{8}\)
\(=0\)
