Nakute is the te-form of nai. Ja nakute is usually used when you want to say "it's not A, it's B". Neko ja nakute, inu desu. (Instead of Neko ja nai. Inu desu.) You can also use it like "okane ga nakute taihen desu" (instead of okane ga nai. Taihen desu.)

'ja nakute'is from 'dewa nai' 'nakute'is from 'nai' so we can say that 'nai'=not eg: benkyoushinai= you don't learn sth tabenai= you don't eat sth