Question

Answer 1

=\(\left(\dfrac{3+\sqrt{5}-3+\sqrt{5}}{9-5}\right):\sqrt{5}\)

=\(\left(\dfrac{2\sqrt{5}}{4}\right).\dfrac{1}{\sqrt{5}}\)

=\(\dfrac{1}{2}\)

Answer 2

\(A=\left(\dfrac{1}{3-\sqrt{5}}-\dfrac{1}{3+\sqrt{5}}\right):\sqrt{5}\)

\(=\left[\dfrac{\left(3+\sqrt{5}\right)-\left(3-\sqrt{5}\right)}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}\right]:\sqrt{5}\)

\(=\left[\dfrac{3+\sqrt{5}-3+\sqrt{5}}{3^2-\left(\sqrt{5}\right)^2}\right]:\sqrt{5}\)

\(=\dfrac{2\sqrt{5}}{6}:\sqrt{5}\)

\(=\dfrac{2\sqrt{5}}{6\sqrt{5}}=\dfrac{1}{3}\)