  The aim of this paper is to present a general algebraic identity. Applying
this identity, we provide several formulas involving the q-binomial
coefficients and the q-harmonic numbers. We also recover some known identities
including an algebraic identity of D. Y. Zheng on q-Ap\'{e}ry numbers and we
establish the q-analog of Euler's formula. The proposed results may have
important applications in the theory of q-supercongruences.
