\(2\sqrt{\dfrac{2}{3}}-4\cdot\sqrt{\dfrac{3}{2}}=2\cdot\sqrt{\dfrac{6}{9}}-4\cdot\sqrt{\dfrac{6}{4}}\)
\(=2\cdot\dfrac{\sqrt{6}}{3}-4\cdot\dfrac{\sqrt{6}}{2}=\dfrac{2\sqrt{6}}{3}-2\sqrt{6}=-\dfrac{4}{3}\sqrt{6}\)
\(\dfrac{5}{2\sqrt{5}}=\dfrac{5\sqrt{5}}{2\cdot5}=\dfrac{\sqrt{5}}{2}\)
\(\dfrac{4}{\sqrt{5}+\sqrt{3}}=\dfrac{4\left(\sqrt{5}-\sqrt{3}\right)}{5-3}=2\left(\sqrt{5}-\sqrt{3}\right)=2\sqrt{5}-2\sqrt{3}\)
\(\dfrac{5\sqrt{48}-3\sqrt{27}+2\sqrt{12}}{\sqrt{3}}\)
\(=\dfrac{5\cdot4\sqrt{3}-3\cdot3\sqrt{3}+2\cdot2\sqrt{3}}{\sqrt{3}}\)
\(=5\cdot4-3\cdot3+2\cdot2=20-9+4=20-5=15\)
\(\dfrac{1}{3+2\sqrt{2}}+\dfrac{4\sqrt{2}-4}{2-\sqrt{2}}\)
\(=\dfrac{3-2\sqrt{2}}{9-8}+\dfrac{\left(4\sqrt{2}-4\right)\left(2+\sqrt{2}\right)}{4-2}\)
\(=3-2\sqrt{2}+\dfrac{4\left(\sqrt{2}-1\right)\left(2+\sqrt{2}\right)}{2}\)
\(=3-2\sqrt{2}+2\sqrt{2}\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)\)
\(=3-2\sqrt{2}+2\sqrt{2}=3\)
