[tex]a] \ \frac{5}{2\sqrt3}\cdot\frac{\sqrt3}{\sqrt3}=\frac{5\sqrt3}{2\sqrt{3^2}}=\frac{5\sqrt3}{2\cdot3}=\frac{5\sqrt3}{6}\\\\b] \ \frac{\sqrt2+1}{\sqrt2-1}\cdot\frac{\sqrt2+1}{\sqrt2+1}=\frac{(\sqrt2+1)^2}{(\sqrt2-1)(\sqrt2+1)}=\frac{2+2\sqrt2+1}{2-1}=3+2\sqrt2\\\\c] \ \frac{\sqrt5-2}{\sqrt5+1}\cdot\frac{\sqrt5-1}{\sqrt5-1}=\frac{(\sqrt5-2)(\sqrt5-1)}{(\sqrt5+1)(\sqrt5-1)}=\frac{5-\sqrt5-2\sqrt5+2}{5-1}=\frac{7-3\sqrt5}{4}[/tex]
