1. **State the problem:** Simplify the expression $$3 + \frac{x^2}{-2x+8}$$. 2. **Identify the formula and rules:** We need to simplify the fraction by factoring and reducing if possible. 3. **Factor the denominator:** $$-2x + 8 = -2(x - 4)$$. 4. **Rewrite the expression:** $$3 + \frac{x^2}{-2(x - 4)}$$. 5. **Check for common factors:** The numerator is $x^2 = x \cdot x$, and the denominator is $-2(x - 4)$. There are no common factors to cancel. 6. **Final simplified form:** $$3 - \frac{x^2}{2(x - 4)}$$ (rewriting the negative sign outside the fraction). This is the simplest form unless further context is given.