>
> ... now I get:
>
> trigsimp(%o11);
> sinh((b - t) w) sinh(t w)
> (%o13) ---------------------------------------------------------
> w cosh((b - t) w) sinh(t w) + w sinh((b - t) w) cosh(t w)
>
> The numerator is what I want; however, the denomenator will simplify to
> w sinh (b w) if the cosh((b - t)w) and sinh((b -t)w) factors are
> expanded.
>
Call that expression ex. You can simplify it using trigsimp(trigreduce(ex))
or factor(trigreduce(ex)), which give slight variants of the result.