"Keep up" has 4 definitions.
Depending on the definition, "keep up" can be inseparable or separable, and associated with certain prepositions. I also include a related expression.
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Definitions
1. To be able to understand or deal with something that is happening or changing very fast.
["keep up with"]
"I try to keep up with the news regarding the pandemic."
"It's difficult to keep up with all the advancements in technology."
2. To stay level or equal with someone or something.
["keep up with"]
"I can't keep up with Ben when we go hiking."
"I couldn't keep up with the workload and almost quit."
This is quite often used in business English.
"It's important to keep up with the competition through innovation and price."
3. To continue to do or have something.
["keep up"]
["keep"] + [something] + ["up"]
"Keep up the good work."
"If you keep up with the payments, you won't get charged interest on your credit card."
Here, you could say "keep the good work up" or "keep up with the good work," but because this is a very common encouragement, it's "keep up the good work."
If you want to use pronouns, then you separate the phrasal verb.
"Keep it up."
Not - "Keep up it."
4. To prevent someone from sleeping.
["keep"] + [someone] + ["up"]
"The neighbour's loud music kept us up until two in the morning."
"Drinking coffee at this hour will keep you up tonight."
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Related expressions
"Keep up appearances" - to pretend to be happier or less poor (etc.) than you really are, because you do not want people to know how bad your situation is.
"They had an unhappy marriage but kept up appearances for the sake of their children."
"She tried to appear cheerful but couldn't keep it up anymore."