Risa

Tuvok and Neelix were individuals but merged into one being, Tuvix. Tuvix had the knowledge and memories of both individuals but existed in one body. One mind. He knew everything the other two did but had his own opinions and reasonings and individuality. The Doctor onboard attempts to find a fix but is unable. He promises to find a solution.

A couple of weeks pass and Tuvix has taken over the duties of both Tuvok and Neelix. He's developing some friendships and relationships. He's even more effective in certain situations than his counterpart would have been due to the unique perspective he has. He's settled in. Then the Doctor informs Captain Janeway and Tuvix that he's discovered a solution and a way to split Tuvix back into Tuvok and Neelix. Everyone is on board except Tuvix who announces he doesn't want to die after gaining his own identity.

Janeway is forced into a horrible position. She wants her friends back but also she wants to respect this lifeform and unique person. She hears from Tuvix and other crew members on what their opinion is. Tuvix obviously is against it. Heavily. Kes, Neelix's girlfriend, desperately wants Neelix back. Tuvok also happens to be Janeways close advisor and close personal friend. After some time, Janeway comes out and asks Tuvix to come with her to sickbay. She is ordering that he undergo the procedure.

Tuvix immediately rebels and starts pleading for his life from various crew members on the bridge. All ignore him and look away. He then attempts to run away but Security officers stop him. Janeway leads him to Sick Bay where he more or less shuts down and just silently judges everyone. The Doctor, aware of Tuvix refusal to undergo the procedure, also refuses to do the procedure. However the procedure is relatively simple to perform. Janeway does the procedure herself, asking the Doctor to step aside. Tuvix is sat down on a bed and Janeway stares him in the eyes. She then splits him back into Tuvok and Neelix. Janeway welcomes the men back and then leaves Sick Bay with a look of self doubt and horror on her face, deeply shaken.

Here's the scene. It's a little edited (a couple moments cut and a weird sound effect added when Tuvix is killed) but you see the broadstrokes.