1. **State the problem:** Simplify the expression $$\frac{5y^2 - 35y}{49 - y^2}$$ and find the restrictions on the variable $y$. 2. **Factor numerator and denominator:** - Numerator: $$5y^2 - 35y = 5y(y - 7)$$ - Denominator: $$49 - y^2 = (7 - y)(7 + y)$$ 3. **Rewrite the expression:** $$\frac{5y(y - 7)}{(7 - y)(7 + y)}$$ 4. **Notice that $7 - y$ can be rewritten as $-(y - 7)$:** $$7 - y = -(y - 7)$$ 5. **Substitute and simplify:** $$\frac{5y(y - 7)}{-(y - 7)(7 + y)} = \frac{5y\cancel{(y - 7)}}{-\cancel{(y - 7)}(7 + y)} = -\frac{5y}{7 + y}$$ 6. **State restrictions:** - Denominator cannot be zero, so: - $$49 - y^2 \neq 0 \Rightarrow (7 - y)(7 + y) \neq 0$$ - $$7 - y \neq 0 \Rightarrow y \neq 7$$ - $$7 + y \neq 0 \Rightarrow y \neq -7$$ - Also, from the canceled factor $y - 7$, $y \neq 7$ to avoid division by zero. **Final simplified expression:** $$-\frac{5y}{7 + y}$$ **Restrictions:** $$y \neq 7, \quad y \neq -7$$