  Background: Precise understanding of nuclear fission is crucial for
experimental and theoretical nuclear physics, astrophysics, and industrial
applications; however, the complete physical mechanics is unresolved due to the
complexities.
  Purpose: In this study, we present a new method to describe the
dynamical-fission process and following prompt-neutron emission, where we
combine the dynamical fission calculation based on the Langevin method and the
Hauser-Feshbach statistical model.
  Methods: Two methods are connected smoothly within the universal charge
distribution and the energy conservation, allowing us to calculate a sequence
of fission dynamics and post-fission phase, including prompt neutron emission.
  Results: Using a certain set of model parameters, we successfully reproduce
the experimental primary-fission yields, total kinetic energy,
independent-fission yields, and prompt neutron emissions for the neutron
induced fission of ${}^{236}$U, a compound nucleus of ${\rm n} + {}^{235}{\rm
U}$. We elucidate the physical mechanism of the characteristic features
observed in previous experiments, such as shell properties. Additionally, we
apply our calculation to two very neutron-rich uranium isotopes, i.e.,
${}^{250}$U and ${}^{255}$U, which are not experimentally confirmed but are
important for r-process nucleosynthesis. Theoretical results indicate that
${}^{250}$U exhibits an asymmetric multiple-peak fission yield distribution,
while the neutron-rich ${}^{255}$U has a single peak due to symmetric fission.
Our method predicts post-neutron emission fragments, where ${}^{250}$U shows a
stronger neutron emissivity than ${}^{255}$U.
  Conclusions: Our framework is highly reproducible in the experiments and
shows that the number of emitted neutrons after fission differs significantly
in neutron-rich uranium fission depending on distributions of fission
variables.
