Remove any remaining drywall tape from the separation. It will easily peel off. Discard the tape.
Sand down any rough areas around the separation with a medium grit-sanding block. Your tape will need a clean and smooth surface for better adhesion. Scrape off any hanging debris with the edge of a drywall knife.
Re-tape the separation with self-adhesive drywall tape. Press the tape firmly onto the Sheetrock to get a good seal.
Apply joint compound over the tape with a trowel. Extend your edge so that the tape is completely covered. Apply a very thin coating of compound and do not over-apply. Let this set until it is hard to the touch, typically about two to four hours depending on the humidity levels in your home.
Sand the joint compound smooth with a fine-grit sanding block. The patch should be level with the rest of the Sheetrock. Sand until the area feels smooth to the touch.
Prime and paint the patched area to match the rest of the room. You will need to prime the area, even if you are using white paint in the room. Paint will stick better to primer than it will to joint compound.