algorithms – The interperation of expected time bound for searches in a hash table

As CLRS book,page 260 stated,

Thus, the total time required for a successful search is $Theta{left(2+alpha/2-alpha/2nright)}=Theta{(1+alpha)}$

I wouldn’t have any problem if the author says the bound is eventually $Theta{(2+alpha/2-alpha/2n)}$ or even $Theta{(1+alpha(1-frac{1}{n}))}$. What kind of logics shall we apply to simplify the original result, i.e, cancelling the factor $1/n$ of $alpha$. What i’ve missed? is anyone got the same confusion?