In this paper we investigate the boundedness character of the positive solutions of the rational difference equation of the form $$x_{n+1}=frac{a_0+{{sum}^k_{j=1}}a_jx_{n-j+1}}{b_0+{{sum}^k_{j=1}}b_jx_{n-j+1}},;;n=0,;1,...$$ where $k{in}N,;and;a_j,b_j,;j=0,;1,...,;k $, are nonnegative numbers such that $b_0+{{sum}^k_{j=1}}b_jx_{n-j+1}>0$ for every $n{in}N{cup}{0}$. In passing we confirm several conjectures recently posed in the paper: E. Camouzis, G. Ladas and E. P. Quinn, On third order rational difference equations(part 6), J. Differ. Equations Appl. 11(8)(2005), 759-777.