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-What are your ages?
-How long had you been together?
-What made you think she was cheating also?
-Could you explain your situation a little more?Thank you again for trusting us with your problem. Please reply as soon as possible so that we can finish answering your question.
we are both 42 ,1 year together, very friendly towards men ignoring me whilst talking to men .holidays alone, her best friend is having affair who she covers for, we have had a stormy relationship from off i wanted more time with her she kept me at arms length, when out in company hardly talks to me and is very flirtatious
Being flirtatious does not mean she is cheating talking to other men is not a sign of cheating, though her actions may have caused you to have doubt that she is being unfaithful to you but you should have talked to her about how you were feeling, you should always communicate with your mate before doing something you will regret. With that being said it's going to be hard to get your ex to come back because she may feel like she was betrayed by you and can no longer trust you so first you have to give her some time to calm down because I'm sure she is angry with you so that is the first thing you need to do. Ask yourself if you think you deserve to have her back after cheating on her be accountable for what you did and show her that you are being accountable and apologize for your indiscretions and reassure her that it won't happen again.
Don't ask her to come back prove to her that you are worth taking back you have do whatever you have to do to show her that you are remorseful about what you did, don't play the blame game and tell her it was because you thought she was cheating is why you did what you did it will only make her more angry. Tell her you were wrong and should have talked things out with you before making such a hasty decision, don't seems desperate that will turn her off even more and it makes you look like your aren't sincere about regretting doing it. Try writing her a short letter. In it, tell her that you agree with the reason she broke up with you, write is a short apology. Tell her you want to apologize for cheating on her. It really was disrespectful to her, and you regret it. Ask her if she could find it in her heart to someday forgive you. Tell her that if time is what she needs that you will give her that but you would like to make it up to her with dinner and possibly talk about things.
You also have to reserve yourself to the fact that she may not want you be and that she just wants to move on from this without you and if she tells you that, that may mean that she still needs more time and is still angry maybe try asking her to start by being friends again and then win her back show her that you changed and want to be a better person.