\(=\sqrt{\dfrac{\left(3\sqrt{5}-1\right)\left(2\sqrt{5}-3\right)}{\left(2\sqrt{5}+3\right)\left(2\sqrt{5}-3\right)}}-\sqrt{\dfrac{\left(11+\sqrt{5}\right)\left(7+2\sqrt{5}\right)}{\left(7+2\sqrt{5}\right)\left(7-2\sqrt{5}\right)}}\)
\(=\sqrt{\dfrac{33-11\sqrt{5}}{11}}-\sqrt{\dfrac{87+29\sqrt{3}}{29}}\)
\(=\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}=\dfrac{\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(\sqrt{5}-1\right)^2}-\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}\)
\(=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)
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