Lee,
I have a similar problem in a few areas of my house. My contractor told me
that it is because the previous owner didn't tape over the crack before
mudding it. What you might need to do is sand down the entire area to the
sheetrock. Then apply fibatape, mud over that and sand it down as even as
possible. After that point you can add texture and paint. It may be tough
too make it look exactly right though. I haven't had too much luck getting
repair textures to match exactly right but it might be "good enough".

Mike

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