\(\dfrac{\sqrt{10}+5\sqrt{3}}{\sqrt{15}+\sqrt{5}}-\dfrac{3}{2\sqrt{2}-\sqrt{5}}+\sqrt{9+4\sqrt{2}}=\dfrac{\sqrt{5}\left(\sqrt{2}+\sqrt{15}\right)}{\sqrt{5}\left(\sqrt{3}+1\right)}-\dfrac{3\left(2\sqrt{2}+\sqrt{5}\right)}{\left(2\sqrt{2}\right)^2-\left(\sqrt{5}\right)^2}+\sqrt{8+2.2\sqrt{2}+1}=\dfrac{\sqrt{15}+\sqrt{2}}{\sqrt{3}+1}-\dfrac{3\left(2\sqrt{2}+\sqrt{5}\right)}{8-5}+\sqrt{\left(2\sqrt{2}+1\right)^2}=\dfrac{\left(\sqrt{15}+\sqrt{2}\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}-\dfrac{3\left(2\sqrt{2}+\sqrt{5}\right)}{3}+2\sqrt{2}+1=\dfrac{3\sqrt{5}-\sqrt{15}+\sqrt{6}-\sqrt{2}}{2}-2\sqrt{2}-\sqrt{5}+2\sqrt{2}+1=\dfrac{3\sqrt{5}-\sqrt{15}+\sqrt{6}-\sqrt{2}}{2}-\sqrt{5}+1=\dfrac{3\sqrt{5}-\sqrt{15}+\sqrt{6}-\sqrt{2}-2\sqrt{5}+2}{2}=\dfrac{\sqrt{5}-\sqrt{15}+\sqrt{6}+2-\sqrt{2}}{2}\)
