Divide and simplify your answer. \[ \frac{x^{2}-6 x}{30} \div \frac{x-6}{5} \] Answer:

To solve the expression \( \frac{x^{2}-6 x}{30} \div \frac{x-6}{5} \), we start by rewriting the division as multiplication by the reciprocal: \[ \frac{x^{2} - 6x}{30} \times \frac{5}{x - 6} \] Next, we can simplify \( x^{2} - 6x \) by factoring it: \[ x^{2} - 6x = x(x - 6) \] Now, substitute this back into the expression: \[ \frac{x(x - 6)}{30} \times \frac{5}{x - 6} \] The \( x - 6 \) terms can be cancelled out since they are common factors (assuming \( x \neq 6 \)): \[ \frac{x \cdot 5}{30} \] This simplifies to: \[ \frac{5x}{30} \] Now reduce \( \frac{5x}{30} \): \[ \frac{x}{6} \] So, the final simplified answer is: \[ \frac{x}{6} \]