I easily repaired by MacBook AC adaptor. Just cut the ends clean, strip back the insulation, attach the inner wire firmly together and carefully tape (I used shrink warp electrical tube), then connect the outer "mesh" (I split it into two and attached the two new "wires" together, and again tape carefully.
It is really just connecting the inner wires together and taping and then the outer mesh wires together and again taping. Make sure it is strong so it cannot pull apart. It looks "funny" because one wire is mesh but it just two wires that need to be connected. I understand the outer mesh is to avoid interference.