AbstractIn this paper, we solve and study the global behavior of the admissible solutions of the difference equation $$\begin{aligned} x_{n+1}=\frac{x_{n}x_{n-2}}{-ax_{n-1}+bx_{n-2}}, \quad n=0,1,\ldots , \end{aligned}$$ x n + 1 = x n x n - 2 - a x n - 1 + b x n - 2 , n = 0 , 1 , ... , where $$a, b>0$$ a , b > 0 and the initial values $$x_{-2}$$ x - 2 , $$x_{-1}$$ x - 1 , $$x_{0}$$ x 0 are real numbers.