a: \(=\dfrac{\sqrt{2}\left(13-4\sqrt{3}\right)}{4\sqrt{3}\left(2\sqrt{3}-1\right)}=\dfrac{1}{2\sqrt{6}}\cdot\left(2\sqrt{3}-1\right)\)
\(=\dfrac{6\sqrt{2}-\sqrt{6}}{12}\)
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