Question

  làm ơn giúp e với ạ 

Answer 1

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

27) \(\dfrac{\sqrt{2}-1}{\sqrt{2}+1}-\dfrac{3-\sqrt{2}}{3+\sqrt{2}}=\dfrac{\left(\sqrt{2}-1\right)^2}{2-1}-\dfrac{\left(3-\sqrt{2}\right)^2}{9-2}=3-2\sqrt{2}-\dfrac{11-6\sqrt{2}}{7}\)

\(=\dfrac{21-14\sqrt{2}-11+6\sqrt{2}}{7}=\dfrac{10-8\sqrt{2}}{7}=\dfrac{2\left(5-4\sqrt{2}\right)}{7}\)

29) \(\dfrac{3}{1-\sqrt{2}}+\dfrac{\sqrt{2}-1}{\sqrt{2}+1}=\dfrac{-3\left(1+\sqrt{2}\right)}{2-1}+\dfrac{\left(\sqrt{2}-1\right)^2}{2-1}=-3-3\sqrt{2}+3-2\sqrt{2}=-5\sqrt{2}\)