1. **State the problem:** Simplify the expression $$\frac{w^2 + w - 56}{w + 8}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor the numerator and denominator if possible, then cancel common factors. 3. **Factor the numerator:** We look for two numbers that multiply to $$-56$$ and add to $$1$$ (the coefficient of $$w$$). These numbers are $$8$$ and $$-7$$, so: $$w^2 + w - 56 = (w + 8)(w - 7)$$. 4. **Rewrite the expression:** $$\frac{(w + 8)(w - 7)}{w + 8}$$. 5. **Cancel the common factor:** $$\frac{\cancel{(w + 8)}(w - 7)}{\cancel{w + 8}} = w - 7$$. 6. **Final answer:** $$w - 7$$. This simplification is valid for $$w \neq -8$$ because the original denominator cannot be zero.