Are these sentences OK?
You were a fool to have quit a job like that.
You were a fool to have left a girl like that. or You were a fool to have broken up with a girl like that.

Question

Are these sentences OK?
You were a fool to have quit a job like that.
You were a fool to have left a girl like that.  or  You were a fool to have broken up with a girl like that.

Answer

Yes, they're all fine.

The last two are ambiguous, because 'like that' could mean 'in that way' or 'that kind of girl', but either way they're good sentences.