Sending children to private schools is perfectly common, and indicative of the separation between the two strata of society. They are physically separated much of the time, particularly with many poor people unable to afford to travel far from their communities, and frequently forbidden from entering the guarded world of the wealthy. The well-off live in a society where menial tasks are undertaken by machines, and whose homes and communities are protected by robots. The poor see little reason for hope. Uprisings and grass-roots action are increasingly common with a number of people able to 'hack' robots to turn them into destructive forces.
Government is under pressure from both ends of the divide.
The poor understandably desire jobs and are requiring a larger and larger welfare outlay. The wealthy however see themselves paying the bulk of the taxes and want more of a return on their money, not to mention increased law and order measures to combat the insurrections from below. Tendency for robot street cleaners etc. Poor can't afford to travel far More local shops etc.