Dyrlægen siger, at hendes hamster ser sund ud, men at pelsen ved poten skal holdes ren.

Dyrlæge means veterinarian / vet.

The ending -en is the usual Danish definite article for many common-gender nouns, so:

• en dyrlæge = a vet
• dyrlægen = the vet

Unlike English, Danish usually attaches the to the end of the noun instead of putting a separate word before it.

Here at means that and introduces a subordinate clause:

• Dyrlægen siger, at ... = The vet says that ...

So the first at introduces what the vet says.

Because there are two coordinated subordinate clauses:

• at hendes hamster ser sund ud
• men at pelsen ved poten skal holdes ren

In English, we often drop the second that, but in Danish repeating at is very natural and often clearer.

So the structure is basically:

• The vet says [that X], but [that Y].

After at, Danish uses subordinate clause word order, which usually means subject before the finite verb:

• hendes hamster ser ...
• pelsen ... skal ...

Compare that with a normal main clause, where Danish is usually verb-second:

• Dyrlægen siger ...

So this sentence shows a common contrast:

• main clause: Dyrlægen siger
• subordinate clause: hendes hamster ser

Because sin/sit/sine refers to the subject of the same clause.

In the clause at hendes hamster ser sund ud, the subject is hamster. So sin hamster would incorrectly suggest the hamster is somehow its own owner.

That is why Danish uses hendes here: it means her hamster, referring to some female person understood from context.

A useful rule:

• use sin/sit/sine only when the possessor is the subject of that same clause
• otherwise use hans / hendes / deres

Se ... ud means to look / appear.

So:

• ser sund ud = looks healthy
• er sund = is healthy

The sentence uses ser sund ud because the meaning is about appearance or how the hamster seems, not a stronger statement of fact.

Because se ud is a multi-part verb, and ud is a particle that often comes later in the clause.

So Danish says:

• hamsteren ser sund ud
• literally: the hamster looks healthy out

You should learn se ud as a unit meaning look / appear. In real sentences, the two parts are often separated.

Because they agree with common-gender singular nouns:

• en hamster → sund
• pelsen (from en pels) → ren

In predicate position, Danish adjectives usually match the noun’s gender and number:

• en hamster er sund
• et dyr er sundt
• dyr er sunde

And similarly:

• pelsen skal holdes ren
• but håret skal holdes rent

So ren agrees with pelsen, not with poten.

Ved usually means by, near, at, around.

So pelsen ved poten means the fur by / around the paw, not necessarily directly on top of it.

If you said på poten, that would sound more like on the paw itself.

So:

• ved poten = near/around the paw
• på poten = on the paw

Because they refer to specific, known parts of the hamster.

• pels = fur
• pelsen = the fur
• pote = paw
• poten = the paw

Danish very often uses the definite form for body parts and other clearly identifiable things when the context makes them specific.

Here, the speaker means a particular area of fur and a particular paw that both speaker and listener can identify.

It means must be kept clean.

Breakdown:

• skal = must / is to / should
• holdes = passive infinitive of holde here, meaning be kept
• ren = clean

So:

• pelsen ved poten skal holdes ren
• the fur by the paw must be kept clean

This is a very common Danish pattern:

• skal + infinitive
• and here the infinitive is passive: holdes

Here it is functioning as an infinitive passive after the modal verb skal.

After modal verbs such as skal, kan, vil, må, Danish normally uses the infinitive without at:

• skal holde = must keep
• skal holdes = must be kept

So even though holdes looks like a present-tense form, in this sentence it is best understood as the verb form required after skal, with passive meaning.

Yes, that is possible, but skal holdes ren is more natural and compact here.

Danish has two common passive types:

• -s passive: holdes
• blive passive: blive holdt

In a sentence like this, especially with general advice or instructions, the -s passive often sounds smoother:

• Pelsen skal holdes ren = the most natural choice here