\(A=\sqrt{\dfrac{3\sqrt{5}-1}{3+2\sqrt{5}}}-\sqrt{\dfrac{\sqrt{5}-1}{\sqrt{5}-2}}\)
\(=\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)
\(=\dfrac{\sqrt{5}-1-\sqrt{5}-1}{\sqrt{2}}\)
\(=-\sqrt{2}\)
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