A method for extracting and separating a rare-earth element by extracting and separating the rare-earth element from an aqueous solution of rare-earth nitrate into n-heptane, with 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester trialkyl methyl ammonium or di-2-ethylhexyl phosphoric acid trialkyl methyl ammonium as an extractant, and n-heptane as a diluent by contacting the aqueous solution of rare-earth nitrate with the extractant and the diluent to extract and separate the rare earth element into n-heptane from the aqueous solution of rare earth nitrate.