"an Arab American man"
Translation:رَجُل أَمْريكِيّ عَرَبِيّ
First: it's ج "j" and not خ "kh". So, it should be written as رجل and not رخل.
Second: in Writing (for the nominative case), we can write the word with diacritics/Harakaat, such as رجلٌ ,رجُلٌ, or رَجُلٌ, and without any Harakaat, ie. رجل. All are same. Harakaat are used to make our reading process easier and to avoid the mistakes.
Third: on daily basis, رجُلٌ rujul(un) is the formal way of Standard Arabic (in the nominative case) while رجُل rajul is in the informal way or slang (as the latter doesn't care much about any Grammar cases).
Nb: you got downvotes for your legitimate question, I give you upvotes :)