We study the boundedness of the difference equation x n + 1 = ( p x n + q x n − 1 ) / ( 1 + x n ) , n = 0 , 1 , … , where q > 1 + p > 1 and the initial values x − 1 , x 0 ∈ ( 0 , + ∞ ) . We show that the solution { x n } n = − 1 ∞ of this equation converges to x ¯ = q + p − 1 if x n ≥ x ¯ or x n ≤ x ¯ for all n ≥ − 1 ; otherwise { x n } n = − 1 ∞ is unbounded. Besides, we obtain the set of all initial values ( x − 1 , x 0 ) ∈ ( 0 , + ∞ ) × ( 0 , + ∞ ) such that the positive solutions { x n } n = − 1 ∞ of this equation are bounded, which answers the open problem 6.10.12 proposed by Kulenović and Ladas (2002).