Question

trục căn thức ở mẫu và rút gọn nếu được

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

Answer 1

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

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

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

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

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

\(=2\)