While you do not want to give your Facebook users exactly the same content as your Twitter followers you can easily add your twitter feed to your Facebook fan page.
Using the Facebook Twitter app located ( http://www.facebook.com/apps/application.php?id=2231777543 ) you simply give Facebook permission to post as you. Then you have the option of selecting where you want the feed to go – your personal profile or your fan page. Select your fan page and save.
Keep in mind each platform like Facebook; Twitter and Linkedin have different audiences and purposes. I call Facebook fan pages the get to know you in a 10-1 ratio of fun things to one marketing post. Twitter is a bit more sharing your knowledge platform and LinkedIn is a build your network of business connections and occasionally share your knowledge with a link to your blog posts or some other link. So think about what you post on twitter and decide if you can share that with your Facebook Fans before you add this feed to your fan page.