You can add water sodium bicarbonate will dissolve in water, To this add ethyl acetate, The organic acids will dissolve in organic solvent. Separate the organic solvent and water using separating funnel.
I. You may want to consider to first selectively and reactively dissolve the sodium bicarbonate component from the three-components powder mixture in dilute HCl/CaCl2 aq. sol.; where the calcium dication avoids the solubilization of both citric and tartaric acids while HCl avoids precipitation of CaCO3. That would leave a simpler two-components powder mixture, of citric and tartaric acids.
II. On the solubility of citric and tartaric acids in water; you may want to see:
Article The Solubility of Citric and Tartaric Acids in Water
Article Solubility of Oxalic, Malonic, Succinic, Adipic, Maleic, Mal...