An exact approach to the problem of x-ray-edge singularities is presented. We devise a transformation that eliminates from the Hamiltonian the process of creation of virtual electron-hole pairs and makes it possible to apply a rigid Fermi-sea picture. The transformed Hamiltonian can be diagonalized exactly. We demonstrate the power of this approach by obtaining the exact analytic form for the emission spectrum in the infinite-hole-mass case. © 1991 The American Physical Society.