Question

Rút gọn:

a) \(\dfrac{3\sqrt{7}+7\sqrt{3}}{\sqrt{21}}\)

b) \(\dfrac{2\sqrt{5}-4\sqrt{10}}{3\sqrt{10}}\)

c) \(\dfrac{3-\sqrt{7}}{3+\sqrt{7}}-\dfrac{3+\sqrt{7}}{3-\sqrt{7}}\)

Answer 1

a. \(\dfrac{3\sqrt{7}+7\sqrt{3}}{\sqrt{21}}=\dfrac{\sqrt{21}\left(\sqrt{3}+\sqrt{7}\right)}{\sqrt{21}}=\sqrt{7}+\sqrt{3}\)

b. \(\dfrac{2\sqrt{5}-4\sqrt{10}}{3\sqrt{10}}=\dfrac{\sqrt{10}\left(\sqrt{2}-4\right)}{3\sqrt{10}}=\dfrac{-4+\sqrt{2}}{3}\)

c. \(\dfrac{3-\sqrt{7}}{3+\sqrt{7}}-\dfrac{3+\sqrt{7}}{3-\sqrt{7}}=\dfrac{\left(3-\sqrt{7}\right)^2}{9-7}-\dfrac{\left(3+\sqrt{7}\right)^2}{9-7}=\dfrac{\left(3-\sqrt{7}-3-\sqrt{7}\right)\left(3-\sqrt{7}+3+\sqrt{7}\right)}{2}=\dfrac{-2\sqrt{7}.6}{2}=-6\sqrt{7}\)