On the difference equation ${ x_{n+1}=\frac{ax_{n}^{2}+bx_{n-1}x_{n-k}}{cx_{n}^{2}+dx_{n-1}x_{n-k}}} - Elabbasy, E. M.; El-Metwally, H.; Elsayed, E.M. (Sarajevo journal of mathematics, 2024)