We derive a new expression for the scattering intensity of fluid mixtures, where one of the components (1) plays an exceptional role. The expression contains two contributions: one from "decorated" particles of component 1-with a modified scattering amplitude-and another one from the sum of the p-1 remaining components. This sum term contains solely direct spatial correlations of the p-1 remaining components, as expressed by their direct correlation functions. The "decoration" of particles 1 is due to the spatial restructuring of the p-1 remaining particle components induced by the presence of particles of component 1. For scattering vector zero (K=0), the decoration can be described in thermodynamic terms as an adsorption of the p-1 kinds of particle species by the particles 1. Our new formula is illustrated with several two-component systems of hard spheres for which the structural functions are (approximately) known. They mimic fluid mixtures of metals and mixtures of colloidal particles. Some calculations are shown for (semi)-dilute solutions of component 1 in a concentrated fluid of particles 2. The results suggest that "decorated" amplitudes and the partial structure factor of component 1 may be obtained, when one substracts simply the scattering of pure component 2 from the total scattering of the mixture. Our formula might be useful for analyzing neutron and x-ray scattering experiments of mixtures of fluid metals with specific attraction forces between the different components and for small-angle scattering of mixtures of colloidal particles.