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勉強{べんきょう}する is one verb. 勉強をする is a phrase.
They don't seem to have any difference in meaning, but the usage may differ.
For 勉強する, an objective can be added:
日本語{にほんご}を勉強する learn Japanese
日本語を勉強をする is wrong
For 勉強をする, adjectives (or words or phrases that can be used as adjectives) ca...