Er ist unersetzlich und hinterlässt eine Lücke, die nicht zu schließen ist.

Questions & Answers about Er ist unersetzlich und hinterlässt eine Lücke, die nicht zu schließen ist.

The lesson is about formal expressions of ability. How does "die nicht zu schließen ist" fit into this?
The structure sein + zu + infinitive is a formal way to express ability or necessity, usually translating to a passive voice in English ("can be" or "must be" done). Here, die nicht zu schließen ist means "that cannot be closed." It acts as a more elegant, higher-register alternative to using können in the passive (die nicht geschlossen werden kann).
Since the lesson covers "vermögen", could I use it here instead of the "sein + zu" structure?
You could, but you would need to change the phrase from passive to active, because vermögen requires an active subject. You would have to say something like eine Lücke, die niemand zu schließen vermag (a gap that no one is able to close).
Why doesn't the verb "hinterlässt" split? Shouldn't the prefix go to the end of the clause?
The verb hinterlassen (to leave behind) is inseparable. While many directional prefixes split (like auf- or ein-), the prefix hinter- behaves like be- or ver- and remains attached to the verb at all times.
How does the word "unersetzlich" break down?
It is built from the verb ersetzen (to replace). By adding the prefix un- (not) and the suffix -lich (which often corresponds to the English "-able"), you get unersetzlich, meaning "irreplaceable."

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