The business letter ___ just ___.

The sentence requires the present perfect passive voice to indicate an action completed in the recent past with relevance to the present. The phrase 'just' often accompanies the present perfect. Therefore, 'has been written' is the correct choice. The structure is Subject + has/have + been + past participle. The business letter (singular subject) takes 'has'. The past participle of 'write' is 'written'. Thus, 'The business letter has just been written.' is grammatically correct.