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Matt James & Rachel Kirkconnell Finally Go Public ... Arm-in-Arm at ESPYs

You can definitely call it a comeback -- Matt James, the first Black 'Bachelor,' and Rachel Kirkconnell making their public debut as a couple ... after the racism controversy that broke them up, and blew up the TV franchise.

The duo was all smiles as they showed up for the ESPYs Saturday night in NYC ... and happily posed for photogs. Although we've known they were back together, they've been laying low.

They looked pretty stylish for their coming out -- Matt, a former college football player, rocked a double-breasted plaid suit, while Rachel went with a very low-cut sheer black gown.

Quick refresher: Matt gave Rachel his final rose, but after pics surfaced of her at an antebellum south, plantation-themed college party ... he broke up with her during the "After the Final Rose" special.

Matt said, “If you don’t understand that something like that is problematic in 2018, there’s a lot of me that you won’t understand.”

Matt framed the split as giving Rachel space to work on herself, and then a few weeks later ... bam! We spotted them out together in Santa Monica -- but they were obviously trying to keep it on the DL, as Matt covered up in shades and a hoodie.

Since then, we've also seen Matt and Rachel hanging out around NYC. So, with last night's debut ... it looks like they've fully worked things out!

Now they can get back to arguing, like every other couple.

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