In a manner that divides, separates, or causes division; in a way that splits things apart.
From the present participle 'dividing' plus the adverbial suffix '-ly,' creating an adverb that describes how an action is performed. This is a rare but grammatically regular English formation.
The '-ly' adverb suffix is so powerful that English speakers can add it to almost any adjective to create an adverb—'dividingly' works perfectly even though it's rarely written, showing how creative the English language can be.
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