In the Lord of the Rings books, Frodo and Gollum's scene at Mount Doom happens a bit differently. This might lead some fans to wonder: would the book version of events have fit the Lord of the Rings movies' story? Or is it better off the way it is? To understand the answers to these questions, it is crucial to understand the differences between the story in the books and that of the movies. There are plenty of similarities too, of course.
Both the Lord of the Rings books and the Lord of the Rings movies have a bittersweet ending. Both versions of the story feature the same main characters, though the arcs of those characters might be different from the page to the screen. Both books and movies tell the tale of Frodo Baggins (Elijah Wood), a simple Hobbit from the Shire and his quest to defeat Sauron and destroy the One Ring. Both feature scenes with Frodo and Gollum (Andy Serkis) at Mount Doom, though how the scenes play out is different.
The Lord of the Rings books are not as dark as the movies, though there are dark moments in both. They also have many noticeable differences in character arcs, including Frodo's. This might explain why the Frodo and Gollum moment is different in the adaptation compared to in the original books. In the Lord of the Rings books, Frodo does somewhat succumb to the power of the Ring. The closer he gets to Mordor, the heavier the Ring gets for him to carry. It is difficult, just as it is in the movies.
At one point, Gollum suggests that Frodo and Sam (Sean Astin) should abandon their quest to destroy the Ring, perhaps even giving it back to him. Frodo warns Gollum that he should not say such a thing because he has sworn a promise by the Ring and the Ring will hold him to it. In fact, it might find a way to twist it so that Gollum's promise by it is his undoing. Frodo also warns Gollum that if he commanded him using the Ring, Gollum would have to obey even if it was to jump from a precipice or fall into the fire. And according to Frodo, that would be what he would want Gollum to do.
Later on in the Lord of the Rings books, Frodo warns Gollum that if he ever touches him again, he'll fall into the fires of Mount Doom. Once they get to Mount Doom, Gollum succeeds in getting the Ring from Frodo and is doing a dance to celebrate regaining his Precious. It is then that Gollum falls into Mount Doom. In the Lord of the Rings movies, the scene plays out differently. Frodo and Gollum struggle for the Ring, and they both almost fall into Mount Doom. Luckily for Frodo, Sam is there to pull him up onto the ledge. Gollum then falls into the fire with his precious Ring.
So would the version from the books have fit the movies' darker tone? It's hard to know. Both versions show that Frodo struggles with the power of the Ring, yet only one of them has him and Gollum fighting till the end for it. That is, of course, the version in the Lord of the Rings movies. In the books, Frodo seems somewhat relieved to be free of the burden of the Ring once it and Gollum fall into the fire. That might have been a somewhat nicer ending for Frodo's character arc, yet it would make fans even more confused when he decides to go to the Undying Lands at the end.
So perhaps the Lord of the Rings movies were right to change that scene a bit. Though it would've been nice to see the book version play out on screen, it might not have fit with Frodo's character arc in the films or the movies' darker tone. The scene where Sam pulls Frodo up is also a nice parallel to the scene where Frodo saves Sam from drowning in The Fellowship of the Ring. And it shows just how important Sam is to Frodo, and to the story overall.
So perhaps the Lord of the Rings movies changing that scene between Frodo and Gollum is a good thing in a way. Since it fits the movies' story better and makes Frodo's character arc in the movies make sense. It also adds a lot to Sam's character, showing how much he is a beacon of hope to both Frodo and the audience. Although the books' version might not have fit in the Lord of the Rings movies, it is good that both versions exist. After all, the books' story is somewhat different to that of the movies, even though the main points are very similar in both. And those who want to can enjoy both versions of the story, in spite of their slight differences.