The two-step mechanism is:
[tex]2A-\ \textgreater \ A_2[/tex] slow
[tex]A_2+B -\ \textgreater \ A_2B[/tex] fast
The overall reaction is the sum of the two reactions:
[tex]2A+A_2+B -\ \textgreater \ A_2+A_2B[/tex]
Now you can cancel the the terms that appear in both sideds:
[tex]2A+B -\ \textgreater \ A_2B[/tex]
The fact that one reaction and the other is fast does not change the product. It does change the spped (rate) of reaction, but that is a different point.
