Question: Return the original user prompt in the "prompt" field. Wrap every mathematical expression, number used in a calculation, equation, fraction, variable, or formula in $...$ for inline math or $$...$$ for display math.
1. **State the problem:** Simplify the expression $$\frac{2x-3x}{4y} \cdot \frac{y}{x^2-9}$$.
2. **Combine and simplify the numerator in the first fraction:**
$$2x - 3x = -x$$
So the expression becomes:
$$\frac{-x}{4y} \cdot \frac{y}{x^2 - 9}$$
3. **Factor the denominator $x^2 - 9$ using the difference of squares:**
$$x^2 - 9 = (x - 3)(x + 3)$$
4. **Rewrite the expression with factored denominator:**
$$\frac{-x}{4y} \cdot \frac{y}{(x - 3)(x + 3)}$$
5. **Multiply the fractions:**
$$\frac{-x \cdot y}{4y \cdot (x - 3)(x + 3)}$$
6. **Cancel common factors $y$ in numerator and denominator:**
$$\frac{-x \cdot \cancel{y}}{4 \cdot \cancel{y} \cdot (x - 3)(x + 3)} = \frac{-x}{4(x - 3)(x + 3)}$$
7. **Final simplified expression:**
$$\boxed{\frac{-x}{4(x - 3)(x + 3)}}$$
This is the simplest form of the given expression.