Question

Rút gọn các biểu thức sau:
a) \(\dfrac{1}{\sqrt{11}+2\sqrt{3}}+\dfrac{1}{\sqrt{23+\sqrt{528}}}\)
b) \(\dfrac{1}{\sqrt{5}-\sqrt{3}}-\dfrac{1}{\sqrt{3}-\sqrt{2}}-\dfrac{2}{\sqrt{5}-\sqrt{2}}\)
c) \(\dfrac{x+\sqrt{x^2-4x}}{x-\sqrt{x^2-4x}}-\dfrac{x-\sqrt{x^2-4x}}{x+\sqrt{x^2-4x}}\)

Answer 1

a: \(=2\sqrt{3}-11+\dfrac{1}{2\sqrt{3}+11}\)

\(=2\sqrt{3}-11+2\sqrt{3}-11=4\sqrt{3}-22\)

b: \(=\dfrac{\sqrt{5}+\sqrt{3}}{2}-\dfrac{\sqrt{3}+\sqrt{2}}{1}-\dfrac{2\sqrt{5}+2\sqrt{2}}{3}\)

\(=\dfrac{3\sqrt{5}+3\sqrt{3}-6\sqrt{3}-6\sqrt{2}-4\sqrt{5}-4\sqrt{2}}{6}\)

\(=\dfrac{-\sqrt{5}-3\sqrt{3}-10\sqrt{2}}{6}\)