Can you sue someone for buying a business that didn't live up to its expectations?

It probably depends on the nature and specificity of the representations and whether they were in writing. The more specific the representations the more likely there is a case.  It also depends on the language of the contract of sale as to whether you can rely on oral representaitons.   Also in transactions of this type, there is a certain level of due diligence required of the buyer.  For example, did you check the books and records of the company before buying to verify the representations.