Est-ce que vous or pouvez

In the sentence Est-ce que vous pouvez parle un peu plus lentement why do you need both est-ce que vous and pouvez - why not just pouvez vous parle etcetera?

Yes, you can either say" Est-ce que vous pouvez parler un peu plus lentement?" or "Pouvez-vous parler un peu plus maintenant?", but why does there need to be only *one* way to say it? Without getting hung up on translations, we have equivalent variations for saying the same thing, like: "Could you speak more slowly?" or "Can you speak more slowly? or "Would it be possible for you to speak more slowly?" Unfortunately, I can't locate an earlier thread, but there is a slight distinction on when to use which, but the gist is that inversions (Pouvez-vous) is more common in formal, written French and "Est-ce que..." is more common in spoken, formal French, although a French speaker is likely to understand what you mean in either case. Anyway, as an aside, I actually asked my tutor back when we started if we could use "vous" for practice. Invariably, my tutor will ask me a question using the "Est-ce que..." form rather than the inversion.

Thanks for the explanation - but can you just use Est-ce que vous and leave out the pouvet in that sentence? Est-ce que vous parle un peu plus lentement?

No, because if you say: "Est-ce que vous parle*z* un peu plus lentement?" you're basically asking, "Are you talking a little slowly?"