solve for all values of p: 3p / (p-5) - 2 / (p+3) = p / (p+3)

Answer 1

3p / (p-5) - 2 / (p+3) = p / (p+3)

Multiply both sides by the LCD, (p-5)(p+3), to get:

3p(p+3) - 2(p-5) = p(p-5)

3p² + 9p - 2p + 10 = p² - 5p

2p² + 12p + 10 = 0

p² + 6p + 5 = 0

(p + 5)(p + 1) = 0

p = -1 or -5