\(\dfrac{3\sqrt{3}-4}{2\sqrt{3}+1}-\sqrt{\dfrac{4+\sqrt{3}}{5-2\sqrt{3}}}\)
\(=\dfrac{\left(3\sqrt{3}-4\right)\left(2\sqrt{3}-1\right)}{\left(2\sqrt{3}+1\right)\left(2\sqrt{3}-1\right)}-\sqrt{\dfrac{\left(4+\sqrt{3}\right)\left(5+2\sqrt{3}\right)}{\left(5-2\sqrt{3}\right)\left(5+2\sqrt{3}\right)}}\)
\(=\dfrac{18-3\sqrt{3}-8\sqrt{3}+4}{12-1}-\sqrt{\dfrac{20+8\sqrt{3}+5\sqrt{3}+12}{25-12}}\)
\(=\dfrac{22-11\sqrt{3}}{11}-\sqrt{\dfrac{32+13\sqrt{3}}{13}}\)
\(=2-\sqrt{3}-\dfrac{\sqrt{13\left(32+13\sqrt{3}\right)}}{13}\)
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