Alex Rodriguez and his fitness instructor girlfriend Jaclyn Cordeiro have split ... TMZ has learned. Jac tells TMZ … "To clarify, Alex and I are currently taking some time apart but there continues to be mutual love, care, and deep respect between us and for our families. We remain supportive of one another, and there is absolutely no animosity, drama, or negative story here." She adds ... "I’m also navigating a serious health matter involving a family member at this time, so my focus is