die Scheidung
divorce
The formal legal dissolution of a marriage.
Nach mehreren Jahren der Trennung haben sie nun die Scheidung eingereicht.
After several years of separation, they have now filed for divorce.

divorce / separation
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divorce
The formal legal dissolution of a marriage.
Nach mehreren Jahren der Trennung haben sie nun die Scheidung eingereicht.
After several years of separation, they have now filed for divorce.

The word 'Scheidung' (divorce/separation) is derived from the verb 'scheiden' (to separate). The ending '-ung' is a typical way of forming feminine nouns from verbs that describe a process or a result.
Die Scheidung des Paares verlief ohne große Streitereien.
The couple's divorce proceeded without major arguments.
In a legal context, 'Scheidung' (divorce) is often used with certain verbs. You can say 'die Scheidung einreichen' (to file for divorce) or 'beantragen' (to apply for/request). The action itself is often expressed with the reflexive verb 'sich scheiden lassen' (to get divorced).
Sie haben nach langer Überlegung die Scheidung eingereicht.
After long consideration, they filed for divorce.
In the figurative meaning, 'Scheidung' (separation) is almost always used with the preposition 'von' + dative. This construction makes clear which two concepts or areas are being separated from each other.
Eine klare Scheidung von Beruflichem und Privatem ist für die mentale Gesundheit wichtig.
A clear separation of professional and private matters is important for mental health.
separation
'die Trennung' and 'die Scheidung' can both refer to the end of a relationship. 'Trennung' is more general: two people end their relationship or no longer live together. This can happen with unmarried couples or also before a divorce. 'Scheidung' is more specific and legal: a marriage is officially ended in court. Learners may confuse the words because both often occur in the context of marriage problems. The important point is: every 'Scheidung' involves a 'Trennung', but not every 'Trennung' is a 'Scheidung'.

Luis sagt, dass die Scheidung seiner Schwester nächsten Monat vor Gericht ist.
Luis says that his sister's divorce will be in court next month.
Wegen der Trennung seiner Eltern zieht das Kind nächste Woche zu seiner Mutter.
Because of his parents' separation, the child is moving in with his mother next week.