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I have heard a lot of positive talk about emacs and I have therefore decided to learn it and start using it. For now, I will mainly be using to write LaTeX documents. I have successfully installed AUCTeX through Homebrew.

I have read that preview-latex should be bundled with AUCTeX but when opening a .tex file in a buffer, I don't have any kind of preview. As far as I can understand, preview-latex should give a second buffer showing a preview of the compiled LaTeX file.

Does anyone have an idea how I can enable this preview?

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Once activated, preview-latex and its documentation will be accessible
via its menus (note that preview-latex requires AUCTeX to be loaded).

Your installation can be broken, or AUCTeX not loaded, or... In any case, you should read the "Introduction" section from the manual.

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No. Preview-latex will preview math expressions in the same buffer. You can "turn it on" in the menus, or by typing C-c C-p C-p which toggles previews at point. It will probably take a bit the first time it's run.

If that doesn't work, you might try adding the following to your .emacs. It's in mine, but I don't think it's actually necessary. It might be a remnant of prehistoric times.

(add-hook 'LaTeX-mode-hook #'LaTeX-preview-setup)
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