I started reading the Inheritance cycle by Christopher Paolini before I started reading J.R.R Tolkien's Lord of the Rings, and I have to say, they seem pretty similar in the books. Of how Eragon uses the Ancient language for magic, and in LOTR someone tells of mysterious people outside of the Spire, using the language of beasts and land, which describes the Ancient language. I don't know, please help.
While Paolini was undeniably influenced by Tolkien, there are several fundamental differences in the mechanics and structure of two worlds that show they're separate. You could write a whole paper on this, but I will list a few.
Perhaps the clearest, most fundamental difference in the worlds is the use of Magic. In Tolkien's legendarium, magic is mostly limited to things like influencing (controlling or inspiring) others, healing or corrupting people, prophecy and visions, crafting and shaping powerful artifacts (like rings and swords), and enhancing power or strength. We occasionally see a few more overt uses, such as when Gandalf uses beams of light to drive away Nazgul, or to disarm Gimli. It's very rare and exceptional to see anything more than that, and usually limited to the Ainur (essentially gods). See here for more information.
On the other hand, in Paolini's world there are comparatively more magic-users, and they can do bright, flashy, impressive things like throw fireballs, freeze water, deflect arrows, kill directly with magic, etc. Magic can be used as a direct, powerful offensive weapon, rather than the mostly supportive and enhancing role it takes in Tolkien's world.
In the Silmarillion (and other histories) we get a clear start-to-finish view of Tolkien's world, including some detailed geography (you can get a brief overview here). This leaves little to no room for a whole new continent (the one the Eragon story takes place in).
Dragons in Tolkien's world are massively powerful, difficult to kill, generally evil, and obsessed with wealth. They can also communicate by speaking. Look for example at Smaug in The Hobbit - he's a pretty typical example of a dragon. Dragons were created at least in some fashion by Morgoth (the biggest baddest big bad guy in Tolkien's world), although it's not clear exactly how. There are also relatively few of them. See here.
Dragons in Paolini's world are much more numerous, potentially much more friendly, and communicate telepathically. They are inherently wild and sometimes violent, but not actually evil. After initial conflict, they learn to coexist peaceably with the other sentient beings.