Ariana Madix Sings 'Everything's Gonna Be Fine' After Cheating Sandal

Ariana Madix is singing her way through any lingering breakup blues she might have -- letting her hair down to belt out some karaoke overseas, and her song choice is an interesting one!!!

The "Vanderpump Rules" star was at The Banshee Labyrinth early Wednesday morning in Edinburgh, Scotland ... and witnesses tell us she was having a good ol' time, even before grabbing the mic.

Ariana got up and sang "Hand in My Pocket" by Alanis Morissette ... which, of course, is all about staying afloat and looking at the bright side in the midst of pain. Sounds familiar.

You can see she really got into the performance, putting a little extra on the line, "Everything's gonna be fine, fine, fine" ... and, at one point, high-fiving a woman in the crowd.

We're told she was there with 2 unknown pals, male and female, and everyone was in a great mood as they chatted before Ariana put on a show.

The generous, and/or drunk, patrons ate it up and showered her with applause.

As you know, she's been going through it since finding out her ex-boyfriend Tom Sandoval was cheating with their costar, Raquel Leviss ... putting an end to their 9-year relationship.

Of course, AM has seemingly moved on with her Coachella bae, Daniel Wai -- and now, she's sending a "fine, fine, fine" message.