1. Stating the problem: Simplify the expression $\frac{-22 - 4xh}{14 - 2xh} \div \frac{22 - 14xh}{x^2 - 8x - 28} \div \frac{x^2 - 6x}{x^2 - 6x}$. 2. Rewrite the expression as multiplication by the reciprocal: $$\frac{-22 - 4xh}{14 - 2xh} \times \frac{x^2 - 8x - 28}{22 - 14xh} \times \frac{x^2 - 6x}{x^2 - 6x}$$ 3. Factor where possible: - Factor numerator and denominator terms: $$-22 - 4xh = -2(11 + 2xh)$$ $$14 - 2xh = 2(7 - xh)$$ $$22 - 14xh = 2(11 - 7xh)$$ $$x^2 - 8x - 28 = (x - 14)(x + 2)$$ $$x^2 - 6x = x(x - 6)$$ 4. Substitute factored forms: $$\frac{-2(11 + 2xh)}{2(7 - xh)} \times \frac{(x - 14)(x + 2)}{2(11 - 7xh)} \times \frac{x(x - 6)}{x(x - 6)}$$ 5. Cancel common factors: - Cancel 2 in numerator and denominator: $$\frac{\cancel{-2}(11 + 2xh)}{\cancel{2}(7 - xh)} \times \frac{(x - 14)(x + 2)}{2(11 - 7xh)} \times 1$$ - Cancel $x(x - 6)$ in last fraction: $$\times 1$$ 6. The expression simplifies to: $$\frac{-(11 + 2xh)}{7 - xh} \times \frac{(x - 14)(x + 2)}{2(11 - 7xh)}$$ 7. Multiply numerators and denominators: Numerator: $$-(11 + 2xh)(x - 14)(x + 2)$$ Denominator: $$2(7 - xh)(11 - 7xh)$$ 8. Final simplified expression: $$\frac{-(11 + 2xh)(x - 14)(x + 2)}{2(7 - xh)(11 - 7xh)}$$