Question

Answer 1

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

\(=2\sqrt{5}+2-2\sqrt{5}+2\)

=4

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

\(=\dfrac{4+2\sqrt{3}+4-2\sqrt{3}}{2}\)

=4

Answer 2

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

2) \(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}+\dfrac{\sqrt{3}-1}{\sqrt{3}+1}=\dfrac{\left(\sqrt{3}+1\right)^2+\left(\sqrt{3}-1\right)^2}{3-1}=\dfrac{3+2\sqrt{3}+1+3-2\sqrt{3}+1}{2}=\dfrac{8}{2}=4\)