$b)\frac{15}{\sqrt{5}}=\frac{15}{\sqrt{5}}\cdot \frac{\sqrt{5}}{\sqrt{5}}=\frac{15\sqrt{5}}{5}=3\sqrt{5}$

$c)\frac{3+\sqrt{2}}{\sqrt{2}}=\frac{3+\sqrt{2}}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{3\sqrt{2}+2}{2}$

$d)\frac{\sqrt{3}-\sqrt{2}}{\sqrt{6}}=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{6}}\cdot \frac{\sqrt{6}}{\sqrt{6}}=\frac{\sqrt{18}-\sqrt{12}}{6}=\frac{\sqrt{9}\cdot \sqrt{2}-\sqrt{4}\cdot \sqrt{3}}{6}=\frac{3\sqrt{2}-2\sqrt{3}}{6}$