A generalization of Elsayed s solution to the difference equation \(x_{n+1}=\frac{ x_{n5}}{1 + x_{n2}x_{n5}}\)

In this paper, we obtain solutions to difference equations of the form \[ x_{n+1}=\frac{ x_{n5}}{a_n+b_n x_{n2}x_{n5}},\]where \((a_{n})\) and \((b_{n})\) are sequences of real numbers. Consequently, a result of Elsayed is generalized. To achieve this, we use Lie symmetry analysis.