In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence $$x_{n+1}={\displaystyle \frac{\alpha x_{n-l}+\beta x_{n-k}}{A{x}_{n-l}+B{x}_{n-k}}},n=0,1,\dots$$ where the parameters $\alpha ,\beta ,A$ and $B$ are positive real numbers and the initial conditions $x_{-p},x_{-p+1},\dots ,x_{-1}$ and $x_0\in (0,\mathrm{\infty })$ where $p=max\{l,k\}$.