mischen
to mix
To combine different substances or ingredients into a uniform mass or liquid.
Für den Cocktail mischt man einfach Saft und Sekt.
For the cocktail, you simply mix juice and sparkling wine.

to mix
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to mix
To combine different substances or ingredients into a uniform mass or liquid.
Für den Cocktail mischt man einfach Saft und Sekt.
For the cocktail, you simply mix juice and sparkling wine.

As a reflexive verb, 'sich mischen' changes its meaning depending on the preposition. 'Sich in etwas (Akkusativ) mischen' means to interfere where one is not wanted. 'Sich unter jemanden (Akkusativ) mischen' means to become part of a group.
Bitte misch dich nicht in meine Angelegenheiten!
Please don't interfere in my affairs!
In its basic meaning, 'mischen' (to mix) is often combined with things that are joined together. Typical phrases are: 'Zutaten mischen' (to mix ingredients), 'Farben mischen' (to mix colors), 'einen Salat mischen' (to toss a salad), or 'Getränke mischen' (to mix drinks).
Der Maler mischt die Farben auf seiner Palette.
The painter mixes the colors on his palette.
In the context of games, 'Karten mischen' (to shuffle cards) is a fixed expression. It means to put the playing cards into a random order before dealing them.
Wer ist als Nächstes mit dem Mischen der Karten dran?
Whose turn is it next to shuffle the cards?
The phrase 'sich in etwas mischen' always follows this pattern: reflexive verb + preposition 'in' + accusative. The object is often an abstract noun such as 'Angelegenheiten' (affairs), 'ein Gespräch' (a conversation), or 'Politik' (politics).
Er hat die schlechte Angewohnheit, sich immer in fremde Gespräche zu mischen.
He has the bad habit of always interfering in other people's conversations.
to separate
'trennen' and 'mischen' are often opposites when it comes to different substances or things. 'trennen' means that you keep things apart or put them back into separate groups. 'mischen' means that you combine different things so that together they form one mass, liquid, or mixture. In cooking, around the house, or in recycling, the difference is important: things that are separated stay individual; things that are mixed are together.

Frau Schwarz mischt Mehl, Eier und Milch, weil sie Pfannkuchen machen möchte.
Mrs. Schwarz mixes flour, eggs, and milk because she wants to make pancakes.
Zu Hause trennen wir Papier, Glas und Plastik in verschiedene Behälter.
At home, we separate paper, glass, and plastic into different containers.