pH Curve in Acid/Base Titrations
Nicolau already outlined it quite clearly in his answer.


  Notice that after mixing the solutions, the number of moles of species containing $\ce{A}$ ($\ce{HA}$ or $\ce{A−}$) is simply $n_A = C_A V_A$


so you have $n_{\ce{HA}} + n_{\ce{A-}} = C_A V_A$


  We will assume that volumes are additive (total volume $V_T = V_A + V_B$)


and given that $[\ce{HA}] = n_{\ce{HA}}/V_T$ and $[\ce{A-}] = n_{\ce{A-}}/V_T$ it should be fairly clear that

$$[\ce{HA}] + [\ce{A-}] = \frac{C_A V_A}{V_A + V_B}$$

as desired.