  We have reexamined the tW+X single top-quark production process which is
important at the LHC contrary to the Tevatron. The special attention was paid
to the treatment of the 2->2[Wt] process and the part of it's next-to-leading
correction: 2->3[Wtb] process. We show that 2->3[Wtb] process has to be
correctly taken into account with a proper subtraction of the top pair
contribution and that it has qualitatively different kinematical distributions
from the 2->2[Wt] process. We present the total cross section of the tW+X
production to be about 62 pb at QCD scale be taken as a top quark mass, suggest
the method of combining Wt and Wtb processes with gauge invariant subtraction
of the tt-bar part which allows to reproduce correct kinematical properties and
perform a proper event simulation of the tW+X process in the whole kinematical
region.
