Find the least common denominator of 5x / x^2 - 7x - 30 and 8 / x^2 - 5x - 24

(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