Perform the operation and express your answer as a single fraction in simplest form. (1)/(3x^2)-(x)/(6)

To perform the operation and express the answer as a single fraction in simplest form, we need to find a common denominator for the two fractions.<br /><br />The common denominator for $\frac{1}{3x^2}$ and $\frac{x}{6}$ is $6x^2$.<br /><br />To rewrite $\frac{1}{3x^2}$ with the common denominator, we multiply the numerator and denominator by 2:<br /><br />$\frac{1}{3x^2} = \frac{1 \cdot 2}{3x^2 \cdot 2} = \frac{2}{6x^2}$<br /><br />To rewrite $\frac{x}{6}$ with the common denominator, we multiply the numerator and denominator by $x^2$:<br /><br />$\frac{x}{6} = \frac{x \cdot x^2}{6 \cdot x^2} = \frac{x^3}{6x^2}$<br /><br />Now we can subtract the two fractions:<br /><br />$\frac{2}{6x^2} - \frac{x^3}{6x^2} = \frac{2 - x^3}{6x^2}$<br /><br />Therefore, the answer is $\frac{2 - x^3}{6x^2}$.