Once you're down for a commitment in a relationship, you set out to a "all for it" mode for your lover and, your lover finally drops the bomb saying "Sorry darling, I think we ain't meant to be together, let's break up.
" My guess is, you'd be devastated because you've invested so much of your time, energy and emotions into it! You're asking the question 4 out of 10 people would - "How to fix a broken relationship with my ex?" Well, the first thing you want to do is take some time off and think it through, see if you really want to fix your relationship, and you're not just being emotionally challenged because you're dumped.
Once you're done you might want to start planning your initiations with your ex.
Start communications casually and not just go ahead calling, texting and emailing and all, that will definitely scare them, they might even ignore you just like that.
After you get in touch, talk on general topic and not specific questions like "Who do you go out with now?".
And please, don't dig up the history of your relationship in conversation if you want to fix a broken relationship! Remember you're now in a fresh start, but instead, use your actions to show that you've change a certain behaviors and habits that they didn't like so you don't even have to tell them about it, they will notice it.
If things go on smoothly, try asking for a date, a place where you can actually talk, a place that is quiet, and not going to a theme or a movie or so.
Better off, if you can get them to a lunch date, so it would be quick and quiet, your ex might not be comfortable being with you for too long.