on the dynamics of a nonautonomous rational difference equation

‎in this paper‎, ‎we study the following nonautonomous rational difference equation‎‎[‎‎y_{n+1}=frac{alpha_n+y_n}{alpha_n+y_{n-k}},quad n=0,1,...‎,‎]‎‎where $left{alpha_nright}_{ngeq0}$ is a bounded sequence of positive numbers‎, ‎$k$ is a positive integer and the initial values $y_{-k},...,y_0$ are positive real numbers‎. ‎we give sufficient conditions under which the unique equilibrium $bar{y}=1$ is globally asymptotically stable‎. ‎furthermore‎, ‎we establish an oscillation result for positive solutions about the equilibrium point‎. ‎our work generalizes and improves earlier results in the literature‎.