Final answer:
To solve the rational equation (p-5)/р = 24/(p+5), cross-multiply to get (p-5)(p+5) = р * 24. Simplify the resulting quadratic equation p^2 - 24р - 25 = 0 and solve for p. Check the solutions by substituting them into the original equation.
Step-by-step explanation:
To solve the rational equation (p-5)/р = 24/(p+5), we can begin by cross-multiplying. This means we multiply the numerator of the left-hand side by the denominator of the right-hand side and vice versa. We get (p-5)(p+5) = р * 24. Solving this equation results in a quadratic equation, which we can simplify and solve for p.
Expanding the left-hand side using the difference of squares identity, we get p^2 - 25 = 24р. Rearranging the equation, we have p^2 - 24р - 25 = 0. Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Once we find the values of p, we can substitute them back into the original equation to check if they satisfy it.
Learn more about Solving rational equations