Complex sentence: Though he privately acknowledged paternity, Brundage took great pains to conceal the existence of these children, concerned that the truth about his extra-marital relationships might damage his chances of election: he requested that his name be kept off the birth certificates.
Split into simpler sentences: Though he privately acknowledged paternity, Brundage took great pains to conceal the existence of these children; he was concerned that the truth about his extra-marital relationships might damage his chances of election. He requested that his name be kept off the birth certificates.