The ammonium hydroxide formula is a topic of debate among many. It is because Ammonium hydroxide is an answer to ammonia in water. Although the name suggests an alkali with the composition of NH4+ and OH− ions, in practicality it's impossible to isolate samples of ammonium hydroxide. Furthermore, the ions also don't account for a significant fraction of the total amount of ammonia.
The accepted chemical formula of ammonium hydroxide is NH4OH wherever ammonium has a charge of +1 and hydroxide has a charge of -1. After they react they both cancel out each other and balance automatically in the end.