Question

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

Answer 1

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

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

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

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

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

\(=2\sqrt{5}\)

Answer 2

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

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

\(=2\sqrt{5}\)