1. **State the problem:** Simplify and solve the equation $$30 = \frac{x^2 - 9}{3 - x} + \frac{x}{2} \cdot \frac{x - 3}{x - 3}$$ where the second fraction simplifies to 1 since numerator and denominator are the same (assuming $x \neq 3$). 2. **Rewrite the equation:** $$30 = \frac{x^2 - 9}{3 - x} + \frac{x}{2} \cdot 1 = \frac{x^2 - 9}{3 - x} + \frac{x}{2}$$ 3. **Factor the numerator:** $$x^2 - 9 = (x - 3)(x + 3)$$ 4. **Rewrite the first fraction:** $$\frac{(x - 3)(x + 3)}{3 - x}$$ Note that $3 - x = -(x - 3)$, so: $$\frac{(x - 3)(x + 3)}{3 - x} = \frac{(x - 3)(x + 3)}{-(x - 3)} = -(x + 3)$$ for $x \neq 3$. 5. **Substitute back:** $$30 = -(x + 3) + \frac{x}{2}$$ 6. **Simplify the right side:** $$30 = -x - 3 + \frac{x}{2}$$ 7. **Combine like terms:** $$-x + \frac{x}{2} = -\frac{2x}{2} + \frac{x}{2} = -\frac{x}{2}$$ So: $$30 = -\frac{x}{2} - 3$$ 8. **Add 3 to both sides:** $$30 + 3 = -\frac{x}{2}$$ $$33 = -\frac{x}{2}$$ 9. **Multiply both sides by -2:** $$-2 \times 33 = x$$ $$x = -66$$ 10. **Check for restrictions:** $x \neq 3$ to avoid division by zero, and $x = -66$ is valid. **Final answer:** $$\boxed{x = -66}$$