Nhân liên hợp:
\(=\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}+1\right)}{\left(\sqrt{\sqrt{3}+1}-1\right)\left(\sqrt{\sqrt{3}+1}-1\right)}-\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}-1\right)}{\left(\sqrt{\sqrt{3}+1}-1\right)\left(\sqrt{\sqrt{3}+1}+1\right)}\)
\(=\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}+1\right)}{\left(\sqrt{\sqrt{3}+1}\right)^2-1^2}-\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}-1\right)}{\left(\sqrt{\sqrt{3}+1}\right)^2-1^2}\)
\(=\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}+1\right)}{\sqrt{3}+1-1}-\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}-1\right)}{\sqrt{3}+1-1}\)
\(=\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}+1\right)}{\sqrt{3}}-\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}-1\right)}{\sqrt{3}}\)
\(=\left(\sqrt{\sqrt{3}+1}+1\right)-\left(\sqrt{\sqrt{3}+1}-1\right)\)
\(=\sqrt{\sqrt{3}+1}+1-\sqrt{\sqrt{3}+1}+1=2\)
