The multi-tracer technique employs a ratio of densities of two differently biased galaxy samples that trace the same underlying matter density field, and was proposed to alleviate the cosmic variance problem. Here we propose a novel application of this approach, applying it to two different tracers one of which is the 21-cm signal of neutral hydrogen from the epochs of reionization and comic dawn. The second tracer is assumed to be a sample of high-redshift galaxies, but the approach can be generalized and applied to other high-redshift tracers. We show that the anisotropy of the ratio of the two density fields can be used to measure the sky-averaged 21-cm signal, probe the spectral energy distribution of radiative sources that drive this signal, and extract large-scale properties of the second tracer, e.g., the galaxy bias. Using simulated 21-cm maps and mock galaxy samples, we find that the method works well for an idealized galaxy survey. However, in the case of a more realistic galaxy survey which only probes highly biased luminous galaxies, the inevitable Poisson noise makes the reconstruction far more challenging. This difficulty can be mitigated with the greater sensitivity of future telescopes along with larger survey volumes.