Question

Answer 1

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

Answer 2

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

Answer 3

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

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

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

= \(4\sqrt{5}\)