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[tex]\frac{3}{\sqrt2}=\frac{3}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\frac{3\sqrt2}{\sqrt{2^2}}=\frac{3\sqrt2}{2}\\\\\frac{5}{\sqrt3}=\frac{5}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac{5\sqrt3}{\sqrt{3^2}}=\frac{5\sqrt3}{3}\\\\\frac{3}{2\sqrt3}=\frac{3}{2\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac{3\sqrt3}{2\sqrt{3^2}}=\frac{3\sqrt3}{2\cdot3}=\frac{\sqrt3}{2}\\\\\frac{2}{3\sqrt5}=\frac{2}{3\sqrt5}\cdot\frac{\sqrt5}{\sqrt5}=\frac{2\sqrt5}{3\sqrt{5^2}}=\frac{2\sqrt5}{3\cdot5}=\frac{2\sqrt5}{15}[/tex]
