\(=\frac{\sqrt{\left(3\sqrt{3}-4\right)\left(2\sqrt{3}+1\right)}}{2\sqrt{3}+1}=\frac{\sqrt{14-5\sqrt{3}}}{2\sqrt{3}+1}=\frac{\sqrt{28-10\sqrt{3}}}{\sqrt{2}\left(2\sqrt{3}+1\right)}=\frac{\sqrt{\left(5-\sqrt{3}\right)^2}}{\sqrt{2}\left(2\sqrt{3}+1\right)}=\frac{5-\sqrt{3}}{\sqrt{2}\left(2\sqrt{3}+1\right)}\)
\(=\frac{\left(5-\sqrt{3}\right)\left(2\sqrt{3}-1\right)}{11\sqrt{2}}=\frac{11\sqrt{3}-11}{11\sqrt{2}}=\frac{\sqrt{3}-1}{\sqrt{2}}=\frac{\sqrt{6}-\sqrt{2}}{2}\)