Question

Rút gọn biểu thức:

1) \(\frac{1}{\sqrt{5}-1}\) - \(\frac{1}{\sqrt{5}+1}\)

2) \(\frac{1}{\sqrt{5}-2}\) + \(\frac{1}{\sqrt{5}+2}\)

3) \(\frac{2+\sqrt{2}}{1+\sqrt{2}}\)

4) \(\frac{2}{4-3\sqrt{2}}\) -\(\frac{2}{4+3\sqrt{2}}\)

Answer 1

\( \begin{align} & 1)\dfrac{1}{\sqrt{5}-1}-\dfrac{1}{\sqrt{5}+1}=\dfrac{\sqrt{5}+1}{{{\left( \sqrt{5} \right)}^{2}}-1}-\dfrac{\sqrt{5}-1}{{{\left( \sqrt{5} \right)}^{2}}-1}=\dfrac{\sqrt{5}+1-\sqrt{5}+1}{4}=\dfrac{1}{2} \\ & 2)\dfrac{1}{\sqrt{5}-2}+\dfrac{1}{\sqrt{5}+2}=\sqrt{5}+2+\sqrt{5}-2=2\sqrt{5} \\ & 3)\dfrac{2+\sqrt{2}}{1+\sqrt{2}}=\dfrac{\sqrt{2}\left( \sqrt{2}+1 \right)}{1+\sqrt{2}}=\sqrt{2} \\ & 4)\dfrac{2}{4-3\sqrt{2}}-\dfrac{2}{4+3\sqrt{2}}=-4-3\sqrt{2}+4-3\sqrt{2}=-6\sqrt{2} \\ \end{align} \)