zusammenarbeiten
to work together
To work together with one or more people on a task or goal.
Die beiden Forscher arbeiten seit Jahren erfolgreich zusammen.
The two researchers have been working together successfully for years.

to collaborate / work together
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to work together
To work together with one or more people on a task or goal.
Die beiden Forscher arbeiten seit Jahren erfolgreich zusammen.
The two researchers have been working together successfully for years.

'Zusammenarbeiten' (to work together) is a separable verb. In a main clause, the prefix 'zusammen' goes at the end. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Wir arbeiten schon lange zusammen.
We have been working together for a long time.
To name the partner, you use the preposition 'mit' (+ dative). To name the project or task, you use 'an' (+ dative).
Sie arbeitet mit einem internationalen Team zusammen.
She works together with an international team.
Whether people or machines are meant can be recognized from the subject of the sentence. If they are people or organizations, it is about cooperation. If they are devices or programs, it is about compatibility.
Diese Software arbeitet perfekt mit unserem System zusammen.
This software works perfectly with our system.
to cooperate
'zusammenarbeiten' and 'kooperieren' both mean that people or groups work together toward a goal. In many sentences, the two words can be used in a similar way. 'zusammenarbeiten' sounds more everyday and fits well at work, at school, or in a team. 'kooperieren' sounds somewhat more formal and is often used for companies, authorities, or organizations. If you are simply talking about working together, 'zusammenarbeiten' is usually more natural. If it should sound more official or is about cooperation between groups, 'kooperieren' fits well.

Morgen arbeite ich mit einem Freund an der Präsentation zusammen.
Tomorrow I am working together with a friend on the presentation.
Die Schule kooperiert mit einem Sportverein aus der Stadt.
The school cooperates with a sports club from the city.