Mariah Carey releases rehearsal video and refers to difficult events of the last few weeks

MariahCareyis back in rehearsals … and belts out a few tunes in a new Instagram post – and refers to her recent difficult weeks.

The singer-songwriter shared the clip on IG early Sunday morning… her first post since announcing that her mother and sister had died on the same day.

In the clip, MC sings “It's Like That” … and sings the notes while a pianist accompanies her. During her mini performance, she beams at the camera.

In the caption, Carey opens up about her feelings… She says she's back at work after “a rough few weeks” – thanking her fans for their continued support and adding that she's looking forward to playing for fans in China and Brazil very soon.

As you know … Mariah's mother Patricia and sister Alison died on the same day about two weeks ago – and Mariah told TMZ she was glad that, despite their complicated relationship, she was still able to spend time with her before she died.

As for Alison, sources familiar with the situation told us She and Mariah had no contact before she died…with drugs playing a big role in their estrangement.

The cause of death of her mother and sister is not yet known.

By the way… nothing has been officially announced yet, but it looks like Mariah will indeed be doing an abbreviated world tour this month—and that’s after fans suspected she would play a few venues in Asia before returning to the U.S. for her holiday tour.