What is the Theory Behind Acid-Base Extraction?

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I'm confused as to what the theory behind this is, I've checked on wikipedia, but it gives a rather convoluted explanation, can anyone clear this up for me?

http://en.wikipedia.org/wiki/Acid-base_extraction

What is this method trying to isolate, only salts? Or is this a valid method for separating other types of compounds?
 

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You may use it to extract any weak acid or base.

The idea is to convert undissociated (hence neutral) acid (or base) dissolved in nonpolar solvent, to charged ions (be it anions for acid or cations for base) which be well soluble in water. Conversion requires neutralization reaction.

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