such a nuisance

  1. My room-mate is such a nuisance. I can’t live on well with him any more.
  2. My room-mate is such a nuisance that I can’t live on well with him any more.
    Are both correct?
    Please comment.
    Thanks.

The standard phrase is ‘get on well’ not ‘live on well’. Your sentences are incorrect.

  1. My room-mate is such a nuisance. I can’t get on well with him any more.
  2. My room-mate is such a nuisance that I can’t get on well with him any more.

‘To do’ is the more natural verb:

  1. My room-mate is such a nuisance. I don’t get on well with him any more.
  2. My room-mate is such a nuisance that I don’t get on well with him any more.

Using ‘live’:

  1. My room-mate is such a nuisance. I can’t live with him any more.
  2. My room-mate is such a nuisance that I can’t live with him any more.