A perturbed hard-sphere-chain (PHSC) equation of state is presented to compute nematicisotropic equilibria for thermotropic liquid crystals, including mixtures. The equation of state consists of an isotropic term and an anisotropic term given by the Maier-Saupe theory whose contribution disappears in the isotropic phase. The isotropic contribution is the recently presented PHSC equation of state for normal fluids and polymers which uses a reference equation of state for athermal hard-sphere chains and a perturbation theory for the squarewell fluid of variable well width. The PHSC equation of state gives excellent correlations of pure-component pressure-volume-temperature data in the isotropic region and, combined with the Maier-Saupe theory, correlates the dependence of nematic-isotropic transition temperature on the pressure. Theory also predicts a nematic-isotropic biphasic region and liquid-liquid phase separation in a temperature-composition diagram of binary mixtures containing a nematic liquid crystal and a normal fluid or polymer. Theory and experiment show good agreement for pure fluids as well as for mixtures.