1. **Problem:** Find values of $x$ for which $\frac{x - 16}{x^2 - 3x}$ is undefined. 2. **Formula:** A rational expression is undefined where the denominator equals zero. 3. **Step:** Set denominator equal to zero: $$x^2 - 3x = 0$$ 4. **Factor:** $$x(x - 3) = 0$$ 5. **Solve:** $$x = 0 \quad \text{or} \quad x = 3$$ 6. **Answer:** Expression undefined at $x=0$ and $x=3$. --- 1. **Problem:** Find values of $x$ for which $\frac{x^2 + 25}{x^2 + 7x + 10}$ is undefined. 2. **Step:** Set denominator equal to zero: $$x^2 + 7x + 10 = 0$$ 3. **Factor:** $$ (x + 5)(x + 2) = 0 $$ 4. **Solve:** $$x = -5 \quad \text{or} \quad x = -2$$ 5. **Answer:** Expression undefined at $x=-5$ and $x=-2$. --- 1. **Problem:** Find values of $x$ for which $\frac{5x(x - 5)}{(x - 5)(x - 2)}$ is undefined. 2. **Step:** Set denominator equal to zero: $$ (x - 5)(x - 2) = 0 $$ 3. **Solve:** $$x = 5 \quad \text{or} \quad x = 2$$ 4. **Answer:** Expression undefined at $x=5$ and $x=2$. **Final summary:** - Expression 1 undefined at $x=0, 3$ - Expression 2 undefined at $x=-5, -2$ - Expression 3 undefined at $x=5, 2$