In this paper we study the behavior of the difference equation xn+1 = αxnx n−l βxn−m + γx n−l , n = 0, 1, ..., where the initial conditions x−r, x−r+1, ..., x0 are arbitrary non zero real numbers where r = max{l, m} is a non-negative integer and α, β and γ are constants. Also, we obtain the solutions of some special cases of this equation. At the end we present some numerical examples to support our theoretical discussion.