Final answer:
To solve the rational equation 1 + 11/p = -24/p², multiply both sides by p² to eliminate the denominators, factorize the resulting quadratic equation, and find the solutions for p.
Step-by-step explanation:
To solve the rational equation 1 + 11/p = -24/p², we can start by multiplying both sides of the equation by p² to eliminate the denominators. This gives us p² + 11p = -24.
Rearranging the equation, we have p² + 11p + 24 = 0. We can then factorize this quadratic equation as (p + 3)(p + 8) = 0. Setting each factor equal to zero, we get p + 3 = 0 or p + 8 = 0. Therefore, the solutions to the equation are p = -3 or p = -8.