Trying to replace s trap with p trap

[DIYduncemaster]

Hey there! Like to start by saying ive found this site super helpful over the past year + and this is my first post, so any advice/help is greatly appreciated.

Ive got a second floor bathroom with an incredibly slow draining (almost stagnant) S trap im attempting to swap out for a p trap. From what i understand everything is connected to the same waste pipe as far as venting is concerned... Both the tub and sink gurgle when im draining one or the other if that tells you anything. Ive got some diagrams im using as a reference including some pictures of said project. It this as sinple as getting an elbow piece and just tying it in with the j bend to make a p trap? Do i need an aav to really fix the slow drainage? Thanks in advance to anyone taking the time to help!

 

[Reach4]

Do i need an aav to really fix the slow drainage?

You need the AAV to prevent smells due to a siphoned-out trap.

The AAV will not help prevent slow drainage of a lavatory or tub. For that, remove the clog. If you run the lavatory faucet full blast down the sink for a while, does that cause backup into the tub? If so, that would show there is a blockage downstream of where the lavatory and tub drains join.

Not sure about gurgling sounds.