1. **State the problem:** Simplify the expression $$\frac{x - 2}{x^2 - 16} = x(x + 4)(x - 4) - x(x + 4)(x - 4) \over x^2 - 4x$$. 2. **Rewrite the expression:** Notice the right side numerator is $$x(x + 4)(x - 4) - x(x + 4)(x - 4)$$ which simplifies to 0 because the two terms are identical and subtract. 3. **Simplify the denominator:** - Factor the denominator on the left side: $$x^2 - 16 = (x - 4)(x + 4)$$. - Factor the denominator on the right side: $$x^2 - 4x = x(x - 4)$$. 4. **Rewrite the equation:** $$\frac{x - 2}{(x - 4)(x + 4)} = \frac{0}{x(x - 4)}$$ 5. **Simplify the right side:** $$\frac{0}{x(x - 4)} = 0$$ 6. **Final simplified equation:** $$\frac{x - 2}{(x - 4)(x + 4)} = 0$$ 7. **Solve for x:** For a fraction to be zero, the numerator must be zero (and denominator not zero): $$x - 2 = 0 \implies x = 2$$ 8. **Check restrictions:** Denominator cannot be zero: - $$x - 4 \neq 0 \implies x \neq 4$$ - $$x + 4 \neq 0 \implies x \neq -4$$ Since $$x=2$$ does not violate these, it is the solution. **Answer:** $$x = 2$$