Question

Tính \(\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}-\sqrt{\frac{3\sqrt{2}+2\sqrt{3}}{3\sqrt{2}-2\sqrt{3}}}\)

Answer 1

\(=\frac{\sqrt{2}\left(\sqrt{3}-\sqrt{2}\right)}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}-\sqrt{\frac{\sqrt{6}\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{6}\left(\sqrt{3}-\sqrt{2}\right)}}\)

\(=\sqrt{6}-2-\sqrt{\frac{\left(\sqrt{3}+\sqrt{2}\right)^2}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}}=\sqrt{6}-2-\left(\sqrt{3}+\sqrt{2}\right)\)