1. **State the problem:** Simplify the expression $$\frac{9m(m - 3)}{m - 5} \div \frac{12mp}{(m - 5)(p + 7)}$$ and express the answer as a fraction in simplest form. 2. **Rewrite the division as multiplication by the reciprocal:** $$\frac{9m(m - 3)}{m - 5} \times \frac{(m - 5)(p + 7)}{12mp}$$ 3. **Cancel common factors:** - The factor $m - 5$ appears in numerator and denominator, so cancel it. - The factor $m$ appears in numerator and denominator, so cancel one $m$. After cancellation, the expression becomes: $$\frac{9(m - 3)(p + 7)}{12p}$$ 4. **Simplify the coefficients:** - $9$ and $12$ have a greatest common divisor of $3$. - Divide numerator and denominator by $3$: $$\frac{3(m - 3)(p + 7)}{4p}$$ 5. **Final simplified fraction:** $$\frac{3(m - 3)(p + 7)}{4p}$$ This is the simplest form of the given expression.