Jennifer Lopez is an amazing multi-tasker ... dividing her attention between ex-hubby Marc Anthony and current BF A-Rod.

JLo was rehearsing with Marc at an historical amphitheatre in the Dominican Republic Saturday, while Alex watched/kept a watchful eye in the VIP section.

There were rumors JLo and Marc had hooked up recently but we're told that's all BS. Fact is ... together and separately, they sell out stadiums.

JLo's main singing gig now is Vegas, where she'll be appearing during the summer.