The rapper and his estranged wife trade public barbs about why they split

The Eminem-Kim Mathers split got nasty – and public – on Thursday when Kim called a Detroit-area radio station to tell her story, the Associated Press reports.

Eminem, 33, and Kim, 31, were married on Jan. 14 for the second time, and the rapper (real name: Marshall Bruce Mathers III) filed for divorce on April 5.

On the morning radio call-in, Kim said that trouble between the two had started even before the wedding.

“He’s having problems with, you know, his problem that he had,” she said, apparently referring to the sleeping-pill addiction for which Eminem sought treatment last summer.

“Right after he came home from his rehab, we started to have a few problems, and I thought it was going to be in our best interest to delay the wedding. But he really pushed it and I thought it was really going to be something that worked this time.”

She hadn’t spoken to Eminem in six weeks, Kim said, but she was still surprised to receive divorce papers this week. “I don’t really necessarily want to get divorced. I was hoping he was going to come home and say, ‘I got us a counselor, let’s go.’ ”

Later that day, Eminem released a statement responding to Kim’s comments.

“The details surrounding both my marriage and subsequent filing for divorce are private, and I had hoped to keep them that way for the sake of my family,” it read.

“A few of Kim’s statements in a radio interview need to be addressed,” the statement continued. “First, her allegations regarding my status post-rehab are both untrue and unfortunate. Second, she was aware that I was filing for divorce.

“We both tried to give our marriage another chance and quickly realized that a wedding doesn’t fix the underlying problems.”

The couple, whose first marriage lasted from 1999 to 2001, have a daughter, Hailie Jade, 10, and adopted Kim’s niece Alaina, 12. Kim also has a daughter, Whitney, 3, from a previous relationship.