Question

Rút gọn biểu thức: \(D=\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}\)

Answer 1

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

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

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

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

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

\(=2\)