der Bruch
fracture
The breaking of a bone in the body; a fracture.
Beim Skifahren hat er sich einen komplizierten Bruch im Bein zugezogen.
He suffered a complicated fracture in his leg while skiing.

break / fracture / fraction
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fracture
The breaking of a bone in the body; a fracture.
Beim Skifahren hat er sich einen komplizierten Bruch im Bein zugezogen.
He suffered a complicated fracture in his leg while skiing.

'Der Bruch' is the noun corresponding to the strong verb 'brechen' (to break). Almost all meanings of 'Bruch' derive from the idea that something breaks—literally or figuratively.
Das Brechen des Glases verursachte einen lauten Knall.
The breaking of the glass caused a loud bang.
'Bruch' is often part of compound nouns that make the meaning more precise. The first word explains what is broken: 'Beinbruch' (broken leg / bone fracture), 'Vertragsbruch' (breach of contract), 'Steinbruch' (quarry).
Ein Ehebruch kann zur Scheidung führen.
Adultery can lead to divorce.
In the medical sense ('Knochenbruch' = bone fracture), the phrase 'sich einen Bruch zuziehen' (to suffer a fracture) is often used.
Beim Fußball hat er sich einen komplizierten Bruch zugezogen.
He suffered a complicated fracture while playing soccer.
When it is about the violation of rules, 'Bruch' often appears with a genitive or in a compound. Typical examples are: 'der Bruch des Gesetzes' (the breaking of the law), 'ein Vertrauensbruch' (a breach of trust), or 'ein Regelbruch' (a rule violation).
Das war ein klarer Bruch seines Versprechens.
That was a clear breach of his promise.
When the end of a relationship is meant, the preposition 'mit' (with) or 'zwischen' (between) is often used: 'der Bruch mit jemandem' (the break with someone) or 'der Bruch zwischen zwei Parteien' (the break between two parties).
Der Streit führte zum Bruch zwischen den beiden Geschäftspartnern.
The argument led to a break between the two business partners.
In the context of mathematics, numbers, numerators, or denominators, 'Bruch' always means 'fraction'.
In der Grundschule lernt man, wie man mit Brüchen rechnet.
In elementary school, you learn how to calculate with fractions.
When stones, rock, or the extraction of materials are being discussed, 'Bruch' means 'Steinbruch' (quarry).
Aus diesem Bruch stammt der Sandstein für die Kirche.
The sandstone for the church comes from this quarry.
separation
'die Trennung' and 'der Bruch' can both mean the end of a relationship, friendship, or cooperation. 'Trennung' usually sounds more neutral and describes the fact that people or groups are no longer together. It can be planned, calm, or also painful. 'Bruch' sounds stronger and often harsher: something ends suddenly, clearly, and often after a conflict. Learners may confuse the words because both describe an ending. When it is about people or groups going separate ways, 'Trennung' fits. When the ending feels abrupt and final, 'Bruch' is more precise.

Der Streit führte zu einem Bruch zwischen den alten Freunden.
The argument led to a break between the old friends.
Die Trennung von ihrem Partner war für sie sehr schwer.
The separation from her partner was very hard for her.