Simplify $\dfrac{\dfrac{1}{\sqrt{2}}}{\dfrac{3}{\sqrt{5}}}$.

To divide by a fraction, multiply by its reciprocal: $\dfrac{1/\sqrt{2}}{3/\sqrt{5}} = \dfrac{1}{\sqrt{2}} \cdot \dfrac{\sqrt{5}}{3} = \dfrac{\sqrt{5}}{3\sqrt{2}}$. This is equivalent to $\dfrac{\sqrt{10}}{6}$ after rationalising the denominator: $\dfrac{\sqrt{5}}{3\sqrt{2}} \cdot \dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{\sqrt{10}}{6}$. But option B as given is the direct simplification. - Trap D reverses numerator/denominator after taking the reciprocal. - Traps A and C apply incorrect simplification steps. The load-bearing principle: dividing by a fraction $=$ multiplying by its reciprocal. The reciprocal of $\dfrac{3}{\sqrt{5}}$ is $\dfrac{\sqrt{5}}{3}$, not $\dfrac{\sqrt{5}}{3}$ inverted again.