Rive was born in Puerto Rico, but his family moved to Palm Beach when he was six years old. He studied psychology at Florida State University between 1981 and 1985 and then became a tennis professional. He had his greatest successes in the men's doubles. In his second year as a professional tennis player, he was in the double-finals of an ATP World Tour tournament , but had to admit defeat to the Spaniards Sergio Casal and Emilio Sánchez in Båstad at the side of Craig Campbell . In the course of his career he reached four times an ATP double finals, but could never win a title; however, he was able to celebrate three title wins between 1989 and 1991 on the ATP Challenger Tour with changing partners. In the individual, his greatest successes were two semi-finals: In Sydney in 1988 he defeated Andrei Olchowski and was defeated by local hero John Fitzgerald ; the following year he failed in the semi-finals in Johannesburg to Paul Chamberlin . He was also in the last sixteen of the Miami Masters in 1988 , where he was defeated by Yannick Noah . He reached the highest ranking in the tennis world rankings in 1988 with position 57 in singles and in 1989 with position 47 in doubles.
His best individual result in a Grand Slam tournament was reaching the third round of the Australian Open in 1988. After victories over Diego Nargiso and Jeremy Bates, he was clearly defeated by Jason Stoltenberg in three sets. In the doubles competition, he reached the round of 16 once each at the Australian Open and the French Open . In mixed he was in the second round of the French Open and Wimbledon in 1991 .
Rive played eleven singles and eight doubles games for the Puerto Rican Davis Cup team between 1992 and 1994 . His greatest success with the team was taking part in the Group II final in Peru . The Peruvians, with Jaime Yzaga as the top player, won the game 5-0.
After the end of his professional career, he returned to Florida State University as an assistant coach, where he worked from 1992 to 1993 and also made up for his bachelor's degree. In 1994 he moved to the University of Alabama as head coach , from 1997 he worked as national coach for the United States Tennis Association , before becoming head coach of Texas Christian University in 2000 . He is married and has two children.