Final answer:
To multiply the given expressions, first multiply the numerators together using the FOIL method, then multiply the denominators. Finally, divide the product of the numerators by the product of the denominators.
Step-by-step explanation:
To multiply the given expressions, we can use the distributive property. First, multiply the numerators together: (c² + 5c + 6) * (c² - 1). This can be simplified by applying the FOIL method: c² * c² + c² * (-1) + 5c * c² + 5c * (-1) + 6 * c² + 6 * (-1). Combine like terms to get: c^4 - c² + 5c³ - 5c + 6c² - 6. Next, multiply the denominators: (c - 1) * (c + 3). Again, this can be simplified using FOIL: c * c + c * 3 - 1 * c - 1 * 3. Simplify to get: c² + 3c - c - 3. Finally, divide the product of the numerators by the product of the denominators: (c^4 - c² + 5c³ - 5c + 6c² - 6) / (c² + 3c - c - 3).