Bài 34:
1. \(=\dfrac{1+\sqrt{2}-1+\sqrt{2}}{1-2}\) \(=\dfrac{2\sqrt{2}}{-1}\) \(=-2\sqrt{2}\)
2. \(=\dfrac{1}{1+\sqrt{5}}-\dfrac{1}{1-\sqrt{5}}\) \(=\dfrac{1-\sqrt{5}-1-\sqrt{5}}{1-5}\) \(=\dfrac{-2\sqrt{5}}{-4}\) \(=\dfrac{\sqrt{5}}{2}\)
3. \(=\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{1}{\sqrt{2}+\sqrt{3}}\) \(=\dfrac{\sqrt{2}+\sqrt{3}-\sqrt{2}+\sqrt{3}}{2-3}\) \(=\dfrac{2\sqrt{3}}{-1}\) \(=-2\sqrt{3}\)
4. \(=\dfrac{\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}}{5-3}\) \(=\dfrac{-2\sqrt{3}}{2}=-\sqrt{3}\)
5. \(=\dfrac{1}{\sqrt{5}+3}+\dfrac{1}{\sqrt{5}-3}\) \(=\dfrac{\sqrt{5}-3+\sqrt{5}+3}{5-9}\) \(=\dfrac{2\sqrt{5}}{-4}\) \(=-\dfrac{\sqrt{5}}{2}\)
6. \(=\dfrac{1}{\sqrt{2}-\sqrt{6}}-\dfrac{1}{\sqrt{2}+\sqrt{6}}\) \(=\dfrac{\sqrt{2}+\sqrt{6}-\sqrt{2}+\sqrt{6}}{2-6}\) \(=\dfrac{2\sqrt{6}}{-4}\) \(=-\dfrac{\sqrt{6}}{2}\)
7. \(=\dfrac{3+2\sqrt{2}-3+2\sqrt{2}}{9-8}\) \(=4\sqrt{2}\)
8. \(=\dfrac{3+2\sqrt{2}}{9-8}+\dfrac{2-\sqrt{5}}{4-5}\) \(=3+2\sqrt{2}+\sqrt{5}-2\) \(=2\sqrt{2}+\sqrt{5}+1\)
