\[\frac{3a^{2}b}{x^{2}} \cdot \frac{x}{ab^{2}}\ :\frac{3a^{2}}{x^{2}b} = \frac{3 \cdot a^{2}b \cdot x \cdot x^{2} \cdot b}{x^{2} \cdot ab^{2} \cdot 3a^{2}} = \frac{x}{a}\]