The two-step mechanism is:
\(2A-\ \textgreater \ A_2\) slow
\(A_2+B -\ \textgreater \ A_2B\) fast
The overall reaction is the sum of the two reactions:
\(2A+A_2+B -\ \textgreater \ A_2+A_2B\)
Now you can cancel the the terms that appear in both sideds:
\(2A+B -\ \textgreater \ A_2B\)
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.
