As part of a deal that would allow Lyft and Uber drivers to service Logan Airport, the ride-sharing companies agreed to let the state run its own background checks. As a result, more than 8,000 current and recent Uber and Lyft drivers in Massachusetts have been banned from driving in the state. The most common reason for rejection was a previously suspended license. Others were rejected due to a violent crime charge, driving offenses, felony convictions and exploitation. The state also identified 51 sex offenders. The ride-sharing companies have, in the past, only considered an employee’s seven-year background, while the newer checks look at a driver’s entire lifetime.