Divide? Segregate?
The word you are looking for is "separate."
The Latin root word that most likely means "separate from the public" is "privatus."
Dual
Separate is the root word for separation.
bisections
The prefix word of "apothecary" is "apo-", which means "away" or "separate."
The word "separate" can be used as both a verb and an adjective. As a verb, it indicates the action of dividing or splitting something into parts. As an adjective, it describes something that is apart or distinct from something else.
The axes separate the plane into four quadrants.
Checks and balances, separate but equal
Bekko ( [別個] & [べっこ] ) means different or separate.
The word for a combination of separate images in one is "collage."
The word joint has one syllable. This means the whole word is the syllable and so there are no syllable breaks.