Question

Tính

\(\dfrac{4}{3\sqrt{3}}-\dfrac{\sqrt{3}-\sqrt{15}}{1-\sqrt{5}}-\dfrac{\sqrt{3}}{1-\sqrt{3}}\)

 

Answer 1

Answer 2

Ta có: \(\dfrac{4}{3\sqrt{3}}-\dfrac{\sqrt{3}-\sqrt{15}}{1-\sqrt{5}}-\dfrac{\sqrt{3}}{1-\sqrt{3}}\)

\(=\dfrac{4\sqrt{3}}{9}-\sqrt{3}+\dfrac{\sqrt{3}\left(1+\sqrt{3}\right)}{2}\)

\(=\dfrac{4\sqrt{3}-9\sqrt{3}}{9}+\dfrac{\sqrt{3}\left(1+\sqrt{3}\right)}{2}\)

\(=\dfrac{-10\sqrt{3}}{18}+\dfrac{9\sqrt{3}\left(1+\sqrt{3}\right)}{18}\)

\(=\dfrac{-10\sqrt{3}+9\sqrt{3}+27}{18}\)

\(=\dfrac{27-\sqrt{3}}{18}\)