On the difference equation xn = xn−2/(bn + cnxn−1xn−2)

We prove that the difference equationxn=xn-2bn+cnxn-1xn-2,n∈N0,where (bn)n∈N0(bn)n∈N0 and (cn)n∈N0(cn)n∈N0 are sequences periodic with period two and the initial values x−2, x−1 are real numbers, can be solved explicitly. Some applications of obtained formulae are given.