When you're on the job, show that you identify with the demands and issues of your organization. You are serious about this and keep your conversations within the boundaries of the business as much as possible. This demonstrates to people your commitment to the business world and to your employer. You'll want to cultivate some privacy about your own domestic issues. Be very selective about what you reveal to co-workers.
Some people tend to build friendships through shared personal difficulties.
But, you do not want to be perceived as a person who doesn't have your life under control. And don't forget that conversations are easily overheard in elevators, cubicles and lunchrooms. Keep your personal revelations generally positive. How you handle anger is, perhaps, the most telling indication of your maturity. This includes anger directed at you as well as your own emotional reactions.