a \(=\dfrac{6}{4+\sqrt{3}-1}=3-\sqrt{3}\)
b: \(=\dfrac{1}{\sqrt{6}}-\dfrac{1}{\sqrt{6}+2}=\dfrac{\sqrt{6}+2-\sqrt{6}}{2\sqrt{3}\left(\sqrt{3}+1\right)}=\dfrac{1}{3+\sqrt{3}}=\dfrac{3-\sqrt{3}}{6}\)
f: \(=\sqrt{\dfrac{14+6\sqrt{5}}{4}}+\sqrt{\dfrac{14-6\sqrt{5}}{4}}\)
\(=\dfrac{3+\sqrt{5}+3-\sqrt{5}}{2}=3\)