rausbringen
to bring out
To transport or accompany someone or something from inside to outside.
Könntest du bitte den Müll rausbringen?
Could you please bring out the trash?

to bring out / release
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to bring out
To transport or accompany someone or something from inside to outside.
Könntest du bitte den Müll rausbringen?
Could you please bring out the trash?

'Rausbringen' (to bring out/release) is a separable verb. The prefix 'raus-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er bringt jeden Abend den Hund raus.
He brings the dog out every evening.
The prefix 'raus' is the colloquial short form of 'heraus' (out). Therefore, 'rausbringen' is used mainly in spoken language and in informal texts.
Wann bringt die Band endlich ihr neues Album raus?
When is the band finally going to release its new album?
In the literal meaning 'nach draußen bringen' (to bring outside), the verb is very often used in fixed everyday combinations, for example 'den Müll rausbringen' (to take out the trash) or 'den Hund rausbringen' (to take the dog out).
Bevor du gehst, könntest du bitte noch den Müll rausbringen?
Before you leave, could you please bring out the trash?
When the context is creative products such as music, books, films, or magazines, 'rausbringen' always means 'veröffentlichen' (to publish/release) or 'auf den Markt bringen' (to bring onto the market).
Der Regisseur will seinen neuen Film nächstes Frühjahr rausbringen.
The director wants to release his new film next spring.
In the meaning 'verwirren' (to confuse), 'rausbringen' always needs an accusative object. This object is the person who is thrown off track.
Deine Zwischenfrage hat mich jetzt total rausgebracht.
Your follow-up question has totally thrown me off now.
In the meaning 'aussprechen' (to say/pronounce), the verb is often used negatively or with a limiting expression to show that someone is having difficulty speaking.
Er war so schüchtern, dass er kaum ein Wort rausbrachte.
He was so shy that he could hardly get out a word.
to remove
'entfernen' and 'rausbringen' can both mean that something is taken away or removed. 'entfernen' is general and neutral: for example, you remove dirt, a stain, or a mistake. 'rausbringen' is more concrete when you bring something from inside to outside. With stains, it can also mean removing them from a fabric; this sounds more colloquial. If only getting rid of something is important, 'entfernen' fits. If the movement outward or getting something out of fabric is emphasized, 'rausbringen' fits.

Sie hat den Kaffeefleck mit kaltem Wasser aus der Bluse rausgebracht.
She got the coffee stain out of the blouse with cold water.
Greta entfernt nach dem Training den Schlamm von ihren Schuhen.
After training, Greta removes the mud from her shoes.