Ta có: \(\frac{\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}}{\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}}\)
\(=\frac{\sqrt{1+2\cdot1\cdot\sqrt{2}+2}+\sqrt{1-2\cdot1\cdot\sqrt{2}+2}}{\sqrt{1+2\cdot1\cdot\sqrt{2}+2}-\sqrt{1-2\cdot1\cdot\sqrt{2}+2}}\)
\(=\frac{\sqrt{\left(1+\sqrt{2}\right)^2}+\sqrt{\left(1-\sqrt{2}\right)^2}}{\sqrt{\left(1+\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}}\)
\(=\frac{1+\sqrt{2}+1-\sqrt{2}}{1+\sqrt{2}-\left(1-\sqrt{2}\right)}\)
\(=\frac{2}{1+\sqrt{2}-1+\sqrt{2}}\)
\(=\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}\)
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