Question

1) Rút gọn biểu thức sau :

1. \(\dfrac{1}{\sqrt{3}+1}\) + \(\dfrac{1}{\sqrt{3}-1}\) - 2\(\sqrt{3}\)

Answer 1

\(\dfrac{1}{\sqrt{3}+1}+\dfrac{1}{\sqrt{3}-1}-2\sqrt{3}\)

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

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

\(=\dfrac{2\sqrt{3}}{2}-2\sqrt{3}\)

\(=\sqrt{3}-2\sqrt{3}=-\sqrt{3}\)