betreuen
to look after
To take care of someone, provide for them, and be responsible for them, e.g. children, sick people, or elderly people.
Die Tagesmutter betreut fünf kleine Kinder.
The childminder looks after five small children.

to look after / supervise
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to look after
To take care of someone, provide for them, and be responsible for them, e.g. children, sick people, or elderly people.
Die Tagesmutter betreut fünf kleine Kinder.
The childminder looks after five small children.

'Betreuen' (to look after / supervise) is an inseparable verb. The prefix 'be-' is never separated from the verb stem, and the past participle is formed without 'ge-': 'betreut'.
Sie hat das Projekt von Anfang an betreut.
She has managed the project from the very beginning.
The verb 'betreuen' (to look after / manage) always needs a direct object in the accusative. You always look after 'someone' or manage 'something'.
Er betreut seine kranke Mutter.
He looks after his sick mother.
The object reveals the exact meaning. If the object is a person (e.g. a child, a patient), 'betreuen' means 'to take care of.' If the object is a thing (e.g. a project, a client), it means 'to be responsible for' or 'to manage.'
Die Ärztin betreut die Patienten auf der Station.
The doctor looks after the patients on the ward.
In the sense of 'to take care of,' 'betreuen' is often combined with people who need help or supervision. Typical phrases are: 'Kinder betreuen' (to look after children), 'Senioren betreuen' (to care for seniors), or 'Patienten betreuen' (to care for patients).
In den Ferien betreut sie die Nachbarskinder.
During the holidays, she looks after the neighborhood children.
In a professional context, 'betreuen' means 'to be responsible for.' Typical objects are: 'ein Projekt betreuen' (to manage a project), 'einen Kunden betreuen' (to handle a client), 'eine Abteilung betreuen' (to manage a department), or also 'eine wissenschaftliche Arbeit betreuen' (to supervise an academic thesis).
Der Professor betreut meine Masterarbeit.
The professor is supervising my master's thesis.
to accept / assume
'sich einer Sache annehmen' and 'betreuen' both have to do with responsibility and help. 'sich einer Sache annehmen' is used when someone starts taking care of a problem, a person, or a task. It emphasizes the decision: someone takes on the matter. 'betreuen' describes more the ongoing work afterward: you regularly look after children, sick people, clients, or a project. So 'annehmen' fits taking on a task, while 'betreuen' fits supporting and caring for something or someone over a period of time.

Mehmet betreut im Büro mehrere Kunden und beantwortet ihre Fragen.
Mehmet handles several clients at the office and answers their questions.
Nach der Beschwerde nimmt sich Frau Becker des Problems sofort an.
After the complaint, Ms. Becker takes care of the problem immediately.