First you said add the radii together, then you gave an example subtracting them, but either way this is incorrect. You divide the larger radius by the smaller radius and add 1

Not quite. With radius 2 and 3 circles, the outer circle would take 2.5 rotations to complete the revolution. You have to set the first circle radius to 1 (divide both radii by the lesser) and then add the radii to calculate the relative circumference of the circle drawn by the motion of the center of the outer circle, so the answer would be calculated like:

2/2 + 3/2 = 5/2 = 2.5