\(\text{a) }\sqrt{5}\left(\sqrt{6}+1\right):\dfrac{\sqrt{2\sqrt{3}+\sqrt{2}}}{\sqrt{2\sqrt{3}-\sqrt{2}}}\\ =\sqrt{5}\left(\sqrt{6}+1\right):\dfrac{2\sqrt{3}+\sqrt{2}}{\sqrt{\left(2\sqrt{3}-\sqrt{2}\right)\left(2\sqrt{3}+\sqrt{2}\right)}}\\ =\sqrt{5}\left(\sqrt{6}+1\right):\dfrac{\sqrt{2}\left(\sqrt{6}+1\right)}{\sqrt{\left(12-2\right)}}\\ =\sqrt{5}\left(\sqrt{6}+1\right):\dfrac{\sqrt{2}\left(\sqrt{6}+1\right)}{\sqrt{10}}\\ =\sqrt{5}\left(\sqrt{6}+1\right)\cdot\dfrac{\sqrt{5}}{\sqrt{6}+1}=5\)
\(\text{b) }\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\\ =\dfrac{\sqrt{2}}{2+\sqrt{4+2\sqrt{3}}}+\dfrac{\sqrt{2}}{2-\sqrt{4-2\sqrt{3}}}\\ =\dfrac{\sqrt{2}}{2+\sqrt{3+1+2\sqrt{3}}}+\dfrac{\sqrt{2}}{2-\sqrt{3+1-2\sqrt{3}}}\\ =\dfrac{\sqrt{2}}{2+\sqrt{\left(\sqrt{3}+1\right)^2}}+\dfrac{\sqrt{2}}{2-\sqrt{\left(\sqrt{3}-1\right)^2}}\\ =\dfrac{\sqrt{2}}{2+\sqrt{3}+1}+\dfrac{\sqrt{2}}{2-\sqrt{3}+1}\\ =\dfrac{\sqrt{2}}{3+\sqrt{3}}+\dfrac{\sqrt{2}}{3-\sqrt{3}}\\ =\dfrac{\sqrt{2}\left(3-\sqrt{3}\right)}{\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)}+\dfrac{\sqrt{2}\left(3+\sqrt{3}\right)}{\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)}\\ =\dfrac{3\sqrt{2}-\sqrt{6}+3\sqrt{2}+\sqrt{6}}{9-3}\\ =\dfrac{6\sqrt{2}}{6}=\sqrt{2}\)
