Rive was born in Puerto Rico, but his family moved to Palm Beach when he was six years old. He studied from 1981 to 1985 psychology at Florida State University and then became a professional tennis player. He had his greatest success in the men's doubles. Already in his second year as a professional tennis player he was in the doubles final of a tournament, the ATP World Tour, had in Båstad on the side of Craig Campbell, however, the Spaniards Sergio Casal and Emilio Sanchez defeated. Throughout his career he reached four times an ATP doubles final, but could never win a title; However, he was able to celebrate with changing partners three title wins between 1989 and 1991 on the ATP Challenger Tour. In some his greatest successes were two semi-finals: In Sydney he defeated in 1988, among others Andrei Olchowski and defeated the local hero John Fitzgerald; the following year he failed in the semifinals of Johannesburg to Paul Chamberlin. In addition, he was in 1988 in the second round of the Miami Masters, where he lost to Yannick Noah. The highest quotation in the tennis world ranking he reached in 1988 with position 57 in the singles and in 1989 with position 47 in doubles.
His best individual result at a Grand Slam tournament was reaching the third round of the Australian Open 1988. According victories over Diego Nargiso and Jeremy Bates was defeated Jason Stoltenberg clear in three sets. In the doubles competition, he once each reached the second round at the Australian Open and the French Open. Mixed In 1991 he stood each in the second round of the French Open and Wimbledon.
Rive played between 1992 and 1994 eleven single and eight double appearances for the Puerto Rican Davis Cup team. His biggest success was with the team to participate in the finals of the Group II in Peru. The being beaten with Jaime Yzaga as top players Peruvians won the match 5-0.
After the end of his professional career, he returned as an assistant coach at Florida State University, where until 1993 he worked in 1992 and also caught up on his bachelor's degree. 1994, he became head coach at the University of Alabama, from 1997 he worked as a coach for the United States Tennis Association before he head coach of the Texas Christian University in 2000. He is married and has two children.