Our master bath doesn't have an exhaust fan and I'd like to add one to help with the humidity. It's the primary bathroom of use upstairs and the 2nd full bath is on the other side of the wall.

Can I use a splitter to tie the other bathroom's exterior vent to the new exhaust? If I did I'd put the splitter closest to the vent to help prevent blow back to the other bathroom. They're both smaller bathrooms (50sqft and 100sqft).

Or is it just better to put it on it's own exhaust vent?