Question

rút gọn

\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)

\(\left(\sqrt{\dfrac{1}{7}}-\sqrt{\dfrac{16}{7}}+\sqrt{7}\right):\sqrt{7}\)

Answer 1

\(a,=\left(\dfrac{\sqrt{7}\left(\sqrt{2}-1\right)}{1-\sqrt{2}}+\dfrac{\sqrt{5}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}\right).\dfrac{\sqrt{7}-\sqrt{5}}{1}\\ =\left(\dfrac{-\sqrt{7}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}+\dfrac{-\sqrt{5}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}\right).\dfrac{\sqrt{7}-\sqrt{5}}{1}\\ =\dfrac{-\sqrt{7}-\sqrt{5}}{1}.\dfrac{\sqrt{7}-\sqrt{5}}{1}=-\left(7-5\right)=-2\)

\(b,=\left(\dfrac{\sqrt{7}}{7}-\dfrac{4\sqrt{7}}{7}+\sqrt{7}\right):\sqrt{7}=\left(\dfrac{\sqrt{7}-4\sqrt{7}+7\sqrt{7}}{7}\right).\dfrac{1}{\sqrt{7}}=\dfrac{4\sqrt{7}}{7}.\dfrac{1}{\sqrt{7}}=\dfrac{4}{7}\)