Consider the rational difference equation \[ x_{n+1}=\frac{ax_{n}+bx_{n-k}}{A+Bx_{n}}~\;\;,~\;n=0,1,\dots \tag{\(*\)} \] where \(a~,b~,A,B\) are positive real numbers, \(k\geq 1\) is a positive integer, and the initial conditions \(x_{-k},~\dots,~x_{-1},~x_{0}\) are nonnegative real numbers. The authors solve an open problem posed by \textit{M. R. S. Kulenović} and \textit{G. Ladas} [Dynamics of second order rational difference equations, Chapman \& Hall / CRC, Boca Raton, FL (2002; Zbl 0981.39011), p. 129]. They prove the following {Theorem}: (a) If \(b\leq A-a,\) then the zero equilibrium of Eq. (\(*\)) is globally asymptotically stable. (b) If \(A-a