  In this paper the asymptotic stability of equilibria and periodic points of
the following higher order rational difference Equation x_{n+1} =(alpha
x_{n-k})/(1+x_{n}...x_{n-k}), k>=1, n=0,1,... is studied where the parameters
?alpha, betta, and gamma are positive real numbers, and the initial conditions
x_{-k}, ..., x_{0} are given arbitrary real numbers. The forbidden set of this
equation is found and then, the order reduction method is used to facilitate
the analysis of its asymptotic dynamics
