Kyle Richards is trying to shut down the gossip about her split from Mauricio Umansky ... by declaring the real reason behind their separation doesn't concern anyone else.

She got choked up as she tackled a fan question on why she's been avoiding the truth about their split during Wednesday night's 'RHOBH' reunion finale .. and as you can see from the clip, it hit a nerve with her!

Even though they've been openly airing their relationship on the show for years, Kyle suddenly flipped the script ... straight-up telling host Andy Cohen, "It's nobody's f***ing business!"

She made it crystal clear that nobody needed the nitty-gritty details about their marriage falling apart after 27 years ... but with her sister Kathy by her side, she did offer a bit more insight into what went down leading up to the split.

Kyle explained like in any marriage, theirs had its highs and lows over the years, especially when kids came into the mix ... but their problems never went away. She also reveals there was a specific incident that shattered her trust in Mauricio.

Andy also asked if the ongoing rumors about Mauricio cheating bothered her ... and she admitted they did, especially when she listened to that nagging voice in her head questioning whether the rumors held any truth.

However, Kyle tried to salvage the relationship 'cause she cared deeply about her family -- only to hit breaking point when her efforts didn't pay off.

Kyle confessed she initially believed the split would be a temporary situation ... but things have now evolved into a surprisingly amicable friendship between them, making it difficult for them to pull the trigger on an official divorce.

It remains to be seen how much Mauricio will reveal about the split on season 2 of his reality show, "Buying Beverly Hills."