På biblioteket er der mere arbejdsro, og derfor har jeg bedre fokus der end på kontoret.

Danish often puts the place, time, or another important element first to set the scene or create contrast.

So:

• På biblioteket = At the library
• then the rest of the sentence tells you what is true there

Starting with På biblioteket highlights the contrast with på kontoret later in the sentence.

A more neutral version would be:

• Der er mere arbejdsro på biblioteket ...

But the given version emphasizes the library first.

This is because Danish is a V2 language: in main clauses, the finite verb normally comes in second position.

The basic structure is:

• Der er mere arbejdsro på biblioteket.
• There is more peace and quiet for working at the library.

When På biblioteket is moved to the front, the verb must stay second:

• På biblioteket er der mere arbejdsro.

So der has not disappeared; it just moves after the verb because På biblioteket now takes the first slot.

Here der does not mean there in the location sense. It is a dummy subject used in existential sentences, like English there is / there are.

So:

• Der er mere arbejdsro = There is more quiet for working

This der is grammatical rather than truly locational.

That matters because later in the sentence there is another der, and that one really does mean there.

This second der is different from the first one.

• first der in er der = dummy/existential there
• second der in fokus der = real location word meaning there

So der in bedre fokus der refers back to på biblioteket.

It avoids repeating the whole phrase:

• ... har jeg bedre fokus der end på kontoret instead of
• ... har jeg bedre fokus på biblioteket end på kontoret

Both are understandable, but the version with der sounds smoother because it avoids repetition.

Arbejdsro is a compound noun:

• arbejde = work
• ro = calm, peace, quiet

Together, arbejdsro means something like:

• peace and quiet to work
• a calm working atmosphere
• freedom from disturbance while working

It is usually treated as an uncountable noun, which is why it fits naturally with mere.

Because arbejdsro is uncountable.

In Danish:

• mere is used with uncountable things or abstract quantities
• flere is used with countable plural nouns

So:

• mere arbejdsro = more peace and quiet
• flere bøger = more books

This is similar to English:

• more quiet
• more books

Again, this is the Danish V2 word order.

After og, the clause begins with derfor in first position. That means the verb must come next:

• og derfor har jeg ...

not:

• og derfor jeg har ...

So the order is:

1. derfor
2. har
3. jeg

This is very common in Danish when an adverb is fronted:

• Derfor har jeg bedre fokus
• Nu går jeg hjem
• I morgen kommer han

Yes, both exist, but they are not exactly the same.

• bedre fokus = better concentration / stronger ability to focus
• mere fokus = more focus, often meaning more attention directed toward something

In this sentence, the idea is about the quality of concentration, so bedre fokus is very natural.

Examples:

• Jeg har bedre fokus om morgenen.
  = I concentrate better in the morning.

• Vi skal have mere fokus på kundeservice.
  = We need to place more focus on customer service.

With places like workplaces and institutions, Danish often uses på where English might use at.

So:

• på biblioteket = at the library
• på kontoret = at the office

Using i is more physically inside-focused:

• i biblioteket = inside the library building/room
• i kontoret = inside the office room

In many contexts:

• på biblioteket sounds more natural for the general place/activity
• på kontoret is the normal way to say at the office

In Danish, the definite article is often attached to the noun as an ending:

• bibliotek = library
• biblioteket = the library
• kontor = office
• kontoret = the office

The sentence uses the definite form because it refers to a known or contextually understood place:

• the library
• the office

This is very normal even when English might sound slightly more general.

End means than.

So:

• bedre fokus der end på kontoret = better focus there than at the office

After end, Danish can use:

• just a phrase: end på kontoret
• or a fuller clause: end jeg har på kontoret

So this sentence could also be expanded as:

• ... derfor har jeg bedre fokus der, end jeg har på kontoret.

The shorter version is more natural in everyday speech.

Because both are being used as general, abstract nouns here.

Danish often leaves out an article with abstract or mass-like nouns, especially after comparatives:

• mere arbejdsro
• bedre fokus

That is similar to English:

• more quiet
• better focus

If you added an article, the meaning would usually become more specific and less natural in this sentence.