Show the validity of the following relations between the species velocities \(v_{\mathrm{A}}\) and \(v_{\mathrm{B}}\) referred to a stationary frame of reference:

\[\boldsymbol{v}_{\mathrm{A}}-\boldsymbol{v}_{\mathrm{B}}=j_{\mathrm{A}}\left(\frac{1}{ho_{\mathrm{A}}}+\frac{1}{ho_{\mathrm{B}}}\right)\]

and

\[\boldsymbol{v}_{\mathrm{A}}-\boldsymbol{v}_{\mathrm{B}}=J_{\mathrm{A}}\left(\frac{1}{C_{\mathrm{A}}}+\frac{1}{C_{\mathrm{B}}}\right)\]