$$A_f=\frac{A_o}{1+\beta A_o}$$ rearranging for $\beta $
I get $A_f(1+\beta A_o)=A_o$
$A_f+A_f\beta A_o=A_o$
$A_f\beta A_o=A_o-A_f$
$$\beta = \frac{A_o-A_f}{A_oA_f}$$
The book shows, I don't see how they get this?
$$\beta=\frac{(A_o/A_f)-1}{A_o}$$
$$A_f=\frac{A_o}{1+\beta A_o}$$ rearranging for $\beta $
I get $A_f(1+\beta A_o)=A_o$
$A_f+A_f\beta A_o=A_o$
$A_f\beta A_o=A_o-A_f$
$$\beta = \frac{A_o-A_f}{A_oA_f}$$
The book shows, I don't see how they get this?
$$\beta=\frac{(A_o/A_f)-1}{A_o}$$
Has to be
$\beta=\frac{(A_o/A_f)-1}{A_o}$
which you get by diving the numerator and denominator of the expression you get by $A_f$
Therefore a typo