If the two solvents can form a negative azeotrope, then distillation of any mixture of those constituents will result in the residue being closer to the composition at the azeotrope than the original mixture. 
For example, if a hydrochloric acid solution contains less than 20.2% hydrogen chloride, boiling the mixture will leave behind a solution that is richer in hydrogen chloride than the original. If the solution initially contains more than 20.2% hydrogen chloride, then boiling will leave behind a solution that is poorer in hydrogen chloride than the original. Boiling of any hydrochloric acid solution long enough will cause the solution left behind to approach the azeotropic ratio. On the other hand, if two solvents can form a positive azeotrope, then distillation of any mixture of those constituents will result in the residue away from the composition at the azeotrope than the original mixture.  For example, if a 50/50 mixture of ethanol and water is distilled once, the distillate will be 80% ethanol and 20% water, which is closer to the azeotropic mixture than the original, which  means the solution left behind will be poorer in ethanol. Distilling the 80/20% mixture produces a distillate that is 87% ethanol and 13% water. Further repeated distillations will produce mixtures that are progressively closer to the azeotropic ratio of 95.5/4.5%. No numbers of distillations will ever result in a distillate that exceeds the azeotropic ratio. Likewise, when distilling a mixture of ethanol and water that is richer in ethanol than the azeotrope, the distillate (contrary to intuition) will be poorer in ethanol than the original but still richer than the azeotrope.
Distillation is one of the primary tools that chemists and chemical engineers use to separate mixtures into their constituents. Because distillation cannot separate the constituents of an azeotrope, the separation of azeotropic mixtures (also called azeotrope breaking) is a topic of considerable interest. Indeed, this difficulty led some early investigators to believe that azeotropes were actually compounds of their constituents. But there are two reasons for believing that this is not the case. One is that the molar ratio of the constituents of an azeotrope is not generally the ratio of small integers. For example, the azeotrope formed by water and acetonitrile contains 2.253 moles (or 9/4 with a relative error of just 2%) of acetonitrile for each mole of water. A more compelling reason for believing that azeotropes are not compounds is, as discussed in the last section, that the composition of an azeotrope can be affected by pressure. Contrast that with a true compound, carbon dioxide for example, which is two moles of oxygen for each mole of carbon no matter what pressure the gas is observed at. That azeotropic composition can be affected by pressure suggests a means by which such a mixture can be separated.