On the Difference Equation xn+1 =xn xn-k /(xn-k+1 a+bxn xn-k )

We show that the difference equation [subscript]xn+1[/subscript] =[subscript]xn[/subscript] [subscript]xn-k[/subscript] /[subscript]xn-k+1[/subscript] (a+b[subscript]xn[/subscript] [subscript]xn-k[/subscript] ),n∈[subscript]...0[/subscript] , where k∈... , the parameters a , b and initial values [subscript]x-i[/subscript] , i=0,k... are real numbers, can be solved in closed form considerably extending the results in the literature. By using obtained formulae, we investigate asymptotic behavior of well-defined solutions of the equation.