Question

Rút gọn

Answer 1

a) \(\dfrac{\sqrt{5}+3}{\sqrt{5}-3}-\dfrac{\sqrt{5}-3}{\sqrt[]{5}+3}=\dfrac{\left(\sqrt{5}+3\right)^2-\left(\sqrt{5}-3\right)^2}{\left(\sqrt{5}-3\right)\left(\sqrt{5}+3\right)}=\dfrac{5+9+6\sqrt[]{5}-5-9+6\sqrt{5}}{5-9}=\dfrac{12\sqrt{5}}{-4}=-3\sqrt{5}\)

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