How does one extract phenol from a mixture of benzoic acid, phenol and butanol?

Answer 1

You could use the following method
distillation.

Answer 2

If you add sodium hydroxide solution, the first two will dissolve and the third won't, so you can use a separating funnel to get rid of the butanol.

I seem to remember that benzoic acid has a dramatic temperature-dependent solubilty, so adding hot dilute HCl will now precipitate phenol, but not benzoic acid. In fact, phenol will merely melt, and form a separate layer. You'll have to check up on this latter part.