Question

Answer 1

\(\dfrac{\sqrt{3}-2}{\sqrt{3}+2}=\dfrac{\left(\sqrt{3}-2\right)^2}{\left(\sqrt{3}-2\right)\left(\sqrt{3}+2\right)}=\dfrac{7-4\sqrt{3}}{3-4}=4\sqrt{3}-7\)

\(\dfrac{2}{1-2\sqrt{5}}=\dfrac{2\left(1+2\sqrt{5}\right)}{\left(1-2\sqrt{5}\right)\left(1+2\sqrt{5}\right)}=\dfrac{2+4\sqrt{5}}{1-\left(2\sqrt{5}\right)^2}=\dfrac{2+4\sqrt{5}}{-19}\)