I purchased music from Apple Music only to discover I can't burn it to a CD
Why can't I copy of the music I just purchased from music onto a cd
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You don't purchase music from Apple Music. Apple Music is a subscription service, and you are only renting the music you don't own it.
To purchase Music to burn onto a CD, you need to do so from the iTunes Store. Each Song will have a price tied to it.
See here: Buy or download music from the iTunes Store in Music on Mac - Apple Support