pH Curve in Acid/Base Titrations

[![Question](https://i.stack.imgur.com/6Wwib.png)](https://i.stack.imgur.com/6Wwib.png)


So I came across a question on the equation of the pH curve, and I wanted to know how the user here arrived at the matter balance equation. Any help would be appreciated! 


Here is the question:


[The reason behind the steep rise in pH in the acid base titration curve](https://chemistry.stackexchange.com/questions/8057/the-reason-behind-the-steep-rise-in-ph-in-the-acid-base-titration-curve/8074#8074)




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 $n\_A = C\_A V\_A$
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so you have $n\_{\ce{HA}} + n\_{\ce{A-}} = C\_A V\_A$



> 
> We will assume that volumes are additive (total volume $V\_T = V\_A + V\_B$)
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> 


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.


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