NOVELTY - The method (100) involves filtering one of a magnetic portion or non-magnetic portion into a course portion and a fine portion. One of the coarse portion or the fine portion is treated (104) with mineral acid to form aqueous mineral acid solution, where mineral acid is nitric acid. The aqueous mineral acid solution is extracted (108) to form organic solution that includes rare earth salts. The organic solution is mixed (112) with water to form aqueous solution that includes the rare earth salts. The rare earth salts are separated (116) from the aqueous solution.    USE - Method for recovering rare earth elements from coal ash such as fly ash and bottom ash. Uses include but are not limited to permanent magnet motors in hybrid vehicles, wind turbines and computer disk drives, hybrid car batteries, compact fluorescent lighting, displays in consumer/defense electronics, industrial catalysts for refining heavier crude oil, automobile catalytic converters, and alloying elements.    ADVANTAGE - The method enables providing ability to build reliable production capabilities and/or supply chain for rare earth elements and/or byproducts, recovering tributyl phosphate after extraction process and recycling tributyl phosphate in future extraction process to minimize amount of tributyl phosphate used in extraction process, and increasing initial concentration by water evaporation to improve extraction efficiency.    DESCRIPTION OF DRAWING(S) - The drawing shows a flow diagram illustrating a method for recovering rare earth elements from coal ash.    Method for recovering rare earth elements from coal ash (100)    Step for treating one of coarse portion or fine portion with mineral acid to form aqueous mineral acid solution (104)    Step for extracting aqueous mineral acid solution to form organic solution that includes rare earth salts (108)    Step for mixing organic solution with water to form aqueous solution that includes rare earth salts (112)    Step for separating rare earth salts from aqueous solution (116)