1. **State the problem:** Simplify the expression $$\frac{C^2 - Cd}{d^2 - de} \div \frac{d^2 - Cd}{cd - ce}$$ 2. **Rewrite division as multiplication by reciprocal:** $$\frac{C^2 - Cd}{d^2 - de} \times \frac{cd - ce}{d^2 - Cd}$$ 3. **Factor each polynomial where possible:** - Numerator 1: $C^2 - Cd = C(C - d)$ - Denominator 1: $d^2 - de = d(d - e)$ - Numerator 2: $cd - ce = c(d - e)$ - Denominator 2: $d^2 - Cd = d^2 - Cd$ (factor out $d$): $d(d - C)$ 4. **Substitute factored forms:** $$\frac{C(C - d)}{d(d - e)} \times \frac{c(d - e)}{d(d - C)}$$ 5. **Multiply numerators and denominators:** $$\frac{C(C - d) \times c(d - e)}{d(d - e) \times d(d - C)}$$ 6. **Cancel common factors:** - $(d - e)$ appears in numerator and denominator - Note that $(C - d)$ and $(d - C)$ are negatives of each other: $(C - d) = -(d - C)$ Rewrite numerator: $$C \times c \times (C - d)(d - e) = Cc (C - d)(d - e)$$ Rewrite denominator: $$d \times d \times (d - e)(d - C) = d^2 (d - e)(d - C)$$ Cancel $(d - e)$: $$\frac{Cc (C - d)}{d^2 (d - C)}$$ Replace $(C - d)$ with $-(d - C)$: $$\frac{Cc \times -(d - C)}{d^2 (d - C)} = \frac{-Cc (d - C)}{d^2 (d - C)}$$ Cancel $(d - C)$: $$\frac{-Cc \cancel{(d - C)}}{d^2 \cancel{(d - C)}} = \frac{-Cc}{d^2}$$ 7. **Final simplified expression:** $$-\frac{Cc}{d^2}$$ This is the simplest form of the given algebraic expression.