Abstract: Processes and systems for separating a mixture including at least one fluorocarboxylic acid and at least one carboxylic acid are provided herein. In some aspects, the present invention relates to processes and systems configured to provide a purified stream of fluorocarboxylic acid and a purified stream of carboxylic acid, even when the mixture includes an azeotrope, a pinch point, and/or a eutectic mixture of the fluorocarboxylic acid and carboxylic acid. Systems as described herein may include, for example, at least one distillation zone and at least one fractional crystallization zone arranged in series and configured to provide highly purified product streams having compositions heretofore unachievable by conventional means.