
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.

to work with
Describes the coordinated and harmonized functioning of technical systems, components, or programs.
Die neue App arbeitet nahtlos mit allen gängigen Betriebssystemen zusammen.
The new app works seamlessly with all common operating systems.
'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 pursuing a goal together. Zusammenarbeiten tends to emphasize ongoing joint work on a task. Kooperieren sounds more formal and often refers to a deliberately agreed, possibly time-limited collaboration between independent people or organizations.

Die Mitarbeiter der beiden Museen arbeiten täglich an der neuen Ausstellung zusammen.
The employees of the two museums work together every day on the new exhibition.
Die beiden Museen kooperieren für eine gemeinsame Ausstellung im nächsten Frühjahr.
The two museums are cooperating on a joint exhibition next spring.