1. **State the problem:** We need to divide the rational expression $ \frac{x^2 - 9x + 20}{3x^2 + 10x - 8} $ by $ \frac{x^2 - 8x + 16}{3x^2 + 13x - 10} $. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal: $$ \frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C} $$ 3. **Apply the rule:** $$ \frac{x^2 - 9x + 20}{3x^2 + 10x - 8} \times \frac{3x^2 + 13x - 10}{x^2 - 8x + 16} $$ 4. **Factor all polynomials:** - Numerator 1: $x^2 - 9x + 20 = (x - 4)(x - 5)$ - Denominator 1: $3x^2 + 10x - 8 = (3x - 2)(x + 4)$ - Numerator 2: $3x^2 + 13x - 10 = (3x - 2)(x + 5)$ - Denominator 2: $x^2 - 8x + 16 = (x - 4)^2$ 5. **Rewrite the expression with factors:** $$ \frac{(x - 4)(x - 5)}{(3x - 2)(x + 4)} \times \frac{(3x - 2)(x + 5)}{(x - 4)^2} $$ 6. **Cancel common factors:** - $3x - 2$ cancels - One $x - 4$ cancels from numerator and denominator Remaining expression: $$ \frac{(x - 5)(x + 5)}{(x + 4)(x - 4)} $$ 7. **Recognize difference of squares:** - Numerator: $(x - 5)(x + 5) = x^2 - 25$ - Denominator: $(x + 4)(x - 4) = x^2 - 16$ 8. **Final simplified form:** $$ \frac{x^2 - 25}{x^2 - 16} $$ This matches option d. **Answer:** D