I keep running into this debate with my thesis advisor. Are both of these forms correct?
It can be seen that both the users are able to...
It can be seen that the both users are able to...
"The both users" is incorrect. The determiner both has already qualified users, so you know who is being referred to. (Refer also to this excellent answer on ELL.) Adding the onto that is similar to saying "the the users". People sometimes do this anyway, such as in the phrase "the both of them", but it's informal.
On the other hand, "both the users" is short for "both of the users". The of is just elided. I would think this is common enough to be acceptable. But if you're in doubt, either use "both of the users" or, as MikeVaughan suggests, "both users".
I think that the article the is extraneous.
It can be seen that both users are able to...
is just fine.
The first example is grammatically correct, the second example is not.
The first sentence in the "Article" wikipedia page says it better than I can: "An article (abbreviated art) is a word that combines with a noun to indicate the type of reference being made by the noun."
You could also say "It can be seen that the two users are able to..." or "It can be seen that each user is able to..."
OT: The real reason that I answer is to object to the weasel-phrase "It can be seen that..."
Can you find a less officious, less self-protective intro? Like "Notice that each user..." or "We see that both users are able..."
Simpler and plainer is better.
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