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

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1. Write the division as multiplication by the reciprocal:
   $$
   \frac{x^2-6x}{30} \div \frac{x-6}{5} = \frac{x^2-6x}{30} \times \frac{5}{x-6}
   $$

2. Factor the numerator $$x^2-6x$$:
   $$
   x^2-6x = x(x-6)
   $$
   So the expression becomes:
   $$
   \frac{x(x-6)}{30} \times \frac{5}{x-6}
   $$

3. Cancel the common factor $$(x-6)$$ (with the condition $$x \neq 6$$):
   $$
   \frac{x\cancel{(x-6)}}{30} \times \frac{5}{\cancel{(x-6)}} = \frac{5x}{30}
   $$

4. Simplify the fraction:
   $$
   \frac{5x}{30} = \frac{x}{6}
   $$

Thus, the simplified answer is:
$$
\frac{x}{6}
$$
The simplified answer is $$ \frac{x}{6} $$.

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