Question

Answer 1

1: \(\dfrac{1}{1-\sqrt{2}}-\dfrac{1}{1+\sqrt{2}}\)

\(=\dfrac{1+\sqrt{2}-1+\sqrt{2}}{1-2}=\dfrac{2\sqrt{2}}{-1}=-2\sqrt{2}\)

2: \(\dfrac{1}{1+\sqrt{5}}+\dfrac{1}{1-\sqrt{5}}\)

\(=\dfrac{1-\sqrt{5}+1+\sqrt{5}}{1-5}=\dfrac{2}{-4}=-\dfrac{1}{2}\)

3: \(\dfrac{1}{\sqrt{5}+\sqrt{3}}-\dfrac{1}{\sqrt{5}-\sqrt{3}}\)

\(=\dfrac{\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}}{2}=\dfrac{-2\sqrt{3}}{2}=-\sqrt{3}\)