Your new client just asked to "friend" you on Facebook. You prefer not to mix your work and social lives, but you don't want to risk hurting a budding business relationship. Should you turn down her invitation to connect?
It's up to you. When in doubt, it's wise to keep work and play separate. Maintain a profile on a business-oriented site, such as LinkedIn, so you can send her a request to connect there, instead. When you do, say, "This is where I stay in touch with work associates. I look forward to working with you!" Don't spend time explaining that you only use Facebook for friends—that will be clear, and there's no need to highlight that she isn't one.
If you do accept friend requests from clients, coworkers, or other business acquaintances on Facebook, be sure that you okay with them seeing all aspects of your page, including photos and comments left by others. You are responsible for policing those. Privacy settings can give you some control, but it's easy to mistake or misunderstand what is visible, so it's better not to rely on them in the first place. Your page can still be about your personal life, but the character traits you display need to be congruent with how your work associates know you.