Effect of a diverging lense on a nearsighted patient

The Problem:
I calculated that a "patient" needs a diverging lense with P=-2 diopters. The patient has a power of accomodation of 2 diopters. This means, that the near point of the patient is 1/2 diopters = 50 cm. Is this correct?

Relevent equations:
1/f = 1/s + 1/s'
1/s(min) = power of accomodation

My attempt
Now, what is the nearpoint of the patient with the glasses on? I thought the powers would add, but 2+-2 =0, so that doesn't make sense. Unless the new near point is 1/4 diopters = 25 cm, but this doesn't seem right. I'm not sure how to be thinking about this problem