\(A=2\dfrac{\left(\sqrt{5+2\sqrt{3}}+\sqrt{5-2\sqrt{3}}\right)}{\sqrt{5+2\sqrt{3}}-\sqrt{5-2\sqrt{3}}}-\dfrac{4+\sqrt{3}+4-\sqrt{3}+2\sqrt{13}}{4+\sqrt{3}-4+\sqrt{3}}\)
\(=\dfrac{2\left(5+2\sqrt{3}+5-2\sqrt{3}+2\sqrt{13}\right)}{5+2\sqrt{3}-5+2\sqrt{3}}-\dfrac{8+2\sqrt{13}}{2\sqrt{3}}\)
\(=\dfrac{10+2\sqrt{13}-8-2\sqrt{13}}{2\sqrt{3}}=\dfrac{1}{\sqrt{3}}\)
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