Closed form formulas for well-defined solutions of the next difference equation \[ x_n=\frac{x_{n-2}x_{n-k-2}}{x_{n-k}(a_n+b_nx_{n-2}x_{n-k-2})},\quad nı\mathbb N_0 \] where $k\in\mathbb N$, $(a_n)_{n\in\mathbb N_0}$, $(b_n)_{n\in\mathbb N_0}$, and initial values $x_{-i}$, $i=\overline{1,k+2}$ are real numbers, are given. Long-term behavior of well-defined solutions of the equation when $(a_n)_{n\in\mathbb N_0}$ and $(b_n)_{n\in\mathbb N_0}$ are constant sequences is described in detail by using the formulas. We also describe the domain of undefinable solutions of the equation. Our results explain and considerably improve some recent results in the literature.