1. **State the problem:** Simplify the expression $$\frac{y^2 + y - 56}{y^2 + 3y - 40}$$. 2. **Factor numerator and denominator:** - Numerator: Find two numbers that multiply to $-56$ and add to $1$ (coefficient of $y$). These numbers are $8$ and $-7$, so: $$y^2 + y - 56 = (y + 8)(y - 7)$$ - Denominator: Find two numbers that multiply to $-40$ and add to $3$. These numbers are $8$ and $-5$, so: $$y^2 + 3y - 40 = (y + 8)(y - 5)$$ 3. **Rewrite the expression with factors:** $$\frac{(y + 8)(y - 7)}{(y + 8)(y - 5)}$$ 4. **Cancel common factors:** $$\frac{\cancel{(y + 8)}(y - 7)}{\cancel{(y + 8)}(y - 5)} = \frac{y - 7}{y - 5}$$ 5. **Final simplified expression:** $$\frac{y - 7}{y - 5}$$ **Note:** The simplification is valid for $y \neq -8$ to avoid division by zero.