Ta có: \(\sqrt{\dfrac{3\sqrt{5}-1}{2\sqrt{5}+3}}-\sqrt{\dfrac{\sqrt{5}+11}{7-2\sqrt{5}}}\)
\(=\sqrt{\dfrac{\left(3\sqrt{5}-1\right)\left(2\sqrt{5}-3\right)}{11}}-\sqrt{\dfrac{\left(11+\sqrt{5}\right)\left(7+2\sqrt{5}\right)}{29}}\)
\(=\sqrt{\dfrac{11\cdot\left(30-9\sqrt{5}-2\sqrt{5}+3\right)}{121}}-\sqrt{29\cdot\left(\dfrac{77+22\sqrt{5}+7\sqrt{5}+20}{841}\right)}\)
\(=\dfrac{\sqrt{363-121\sqrt{5}}}{11}+\dfrac{\sqrt{2813+841\sqrt{5}}}{29}\)
\(=\dfrac{\sqrt{726-242\sqrt{5}}}{11\sqrt{2}}+\dfrac{\sqrt{5626+1682\sqrt{5}}}{29\sqrt{2}}\)