3 / ( (r - 1)(r + 2) ) = 1
3 = (r - 1)(r + 2)
r^2 + r - 2 = 3
r^2 + r = 5
There's a 1 on the r in the middle. Half of 1 is 1/2. 1/2 squared is 1/4
r^2 + r + 1/4 = 5 + 1/4
(r + 1/2)^2 = 21/4
r + 1/2 = +- sqrt(21/4)
r + 1/2 = +-sqrt(21)/2
r = +-sqrt(21)/2 - 1/2
r = (+-sqrt(21) - 1) / 2
r = (sqrt(21) - 1) / 2 or r = (-sqrt(21) - 1) / 2