there are 2 rings of charge, radius R on the x axis separated by a distance R, find the potential and E field.

so don't you have to calculate the field to the left of the 2 rings, in between the 2 rings and to the right? I get these answers for the E field which by symmetry points only on the x axis away from the rings. in the area to the left and to the right of the rings the 2 fields will add and in between there will be some subtraction

I think my calculation is off here, the field for one ring, positive lambda charge pointing away from the ring is?