Nick Lachey, Jessica Simpson Split

"After three years of marriage, and careful thought and consideration, we have decided to part ways," the couple says

Jessica Simpson, 25, and Nick Lachey, 32, are going their separate ways, the couple announced in a statement Wednesday.

“After three years of marriage, and careful thought and consideration, we have decided to part ways,” the statement says. “This is the mutual decision of two people with an enormous amount of respect and admiration for each other. We hope that you respect our privacy during this difficult time.”

Reports that their union was in trouble began surfacing last October following a wild bachelor party attended by Lachey. The couple denied those stories, with Simpson telling PEOPLE: “Our relationship is better than it’s ever been.”

Over the winter, the pair spent much of their time apart while Simpson was in Louisiana filming her movie debut as Daisy Duke in Dukes of Hazzard and Lachey worked on solo music projects.

But the couple reunited in the spring and shot down persistent rumors of a marital rift as they were seen out and about shopping, cuddling and clubbing together.

Still, by July more reports surfaced that the marriage was kaput. Jessica’s father and manager, Joe Simpson, stepped forward to defend the couple. “Do they fight? Hell yes, they fight. Have there been moments when Nick has wanted to leave Jessica or Jess has wanted to leave Nick? Absolutely,” said the elder Simpson, explaining that the squabbles were not to be interpreted as a sign of major trouble in the union.

“(It’s the) same with me and my wife,” Joe insisted. “If fighting is a sign of divorce, then we’re all going to get divorced. My wife and I have been married 27 years. We’ve been at the edge of divorce for 26 of them.”

For her part, Jessica said that while she and Nick occasionally were seen squabbling, “You don’t want to marry somebody who’s just like you. So there are always going to be conflicts. An argument now and then is good. It means that we’re communicating.”

And yet, the stories of a Simpson-Lachey rift continued to circulate. On Aug. 3, New York Post gossip columnist Cindy Adams went so far as to print that the couple had “hired divorce lawyers, already drawn up divorce papers, even actually signed divorce papers” – prompting Lachey to respond publicly. Cohosting TV’s Live With Regis and Kelly with Kelly Ripa the day of Adams’s item, Lachey said that everything was “absolutely wonderful” in his relationship with Simpson. He also denied being jealous of Simpson’s movie career.

The pair first met at the Hollywood Christmas Parade in 1998, when Lachey was still a member of the pop group 98 Degrees. He said what really made him fall for Simpson was seeing her perform. “I watched her sing and saw the way people responded,” he said at the time.

Within weeks of meeting her, he was telling fellow band members, “I’m going to marry that girl.” In February 2002 Lachey chartered a yacht in Hawaii and proposed to Simpson as the sun set on the Pacific.

They married in a lavish ceremony on Oct. 26, 2002, in Austin, Texas. Their new life together – mostly spent at their home in Calabasas, Calif. – was chronicled on MTV’s reality series Newlyweds: Nick and Jessica.

Before getting married, the couple briefly broke up in 2001 then decided to reunite after Sept. 11. “Nick was patiently waiting for me to grow up a little,” Simpson told PEOPLE at the time. “I knew that I never, ever wanted to be away from Nick for the rest of my life.”

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