Answer:
(x - 10)(x - 8)(x + 3) = x³ - 15x² + 34x + 240
Step-by-step explanation:
To find the common denominator of the two fractions, you need to first factor the polynomials:
x² - 7x - 30 = (x - 10)(x + 3)
x² - 5x - 24 = (x - 8)(x + 3)
Since the common binomial is (x + 3), both denominators would need to also include (x - 10) and (x - 8). So, the full common denominator is:
(x + 3)(x - 10)(x - 8)
When you multiply these polynomials out using distribution and FOIL:
x³ - 15x² + 34x + 240
