Calculus help with critical numbers

Find the critical numbers of the function.
h(p) = (p - 3)/(p^2 + 1)

need an explanation thanks!

You need to find p such that h'(p) = 0

h'(p) = (1 * (p^2 + 1) - (p - 3) * 2p) / (p^2 + 1)^2
h'(p) = (p^2 + 1 - 2p^2 + 6p) / (p^2 + 1)^2
h'(p) = (-p^2 + 6p + 1) / (p^2 + 1)^2

h'(p) = 0
(-p^2 + 6p + 1) / (p^2 + 1)^2 = 0
-p^2 + 6p + 1 = 0
p^2 - 6p - 1 = 0

p = (6 ± √(36+4)) / 2
p = (6 ± 2√10) / 2
p = 3 ± √10

To find critical numbers of a function:

1. Take the first derivative of the function
2. Equal it to ZERO
3. Solve the resultant equation
4. Plug the solution (x) into the original function to find y