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You would expect to observe a doublet if the proton HA would interact only with the proton HM (n = 1, and therefore M = 2)!

However, the protons HX are also separated from HA by only three bonds
ClCH = CH - CH2Cl
M   A   X
), and they also should contribute to the splitting of the energy levels of

You might want to check the summary on page 95 for additional explanations!