The main objective of this paper is to study some qualitative behavior of the solutions of the two difference equations $$x_{n+1}=ax_{n-k}+bx_{n-k}/(cx_n+\delta dx_{n-k}),\ \ n=0,1,2,\dots,$$ where the initial conditions $x_{−k}, \dots , x_{−1}, x_0$ are arbitrary positive real numbers and the coefficients $a, b, c$ and $d$ are positive constants, while $k$ is a positive integer number and $\sigma = \pm 1$. Some numerical examples are given to illustrate our results.