To simplify the expression (p3 + 5p2 - 24p) / (9p(p + 8)), first factor out any common terms from the numerator and denominator:
p3 + 5p2 - 24p = p(p2 + 5p - 24) = p(p + 8)(p - 3)
Now, rewrite the expression as:
(p(p + 8)(p - 3)) / (9p(p + 8))
Next, cancel out the common factors from the numerator and denominator:
(p(p + 8)(p - 3)) / (9p(p + 8)) = (p - 3) / 9p
Therefore, the simplified expression is (p - 3) / (9p).
