I was reading about lead compensator from a website but i am not able to understand how they have extracted zero and pole from transfer function of lead compensator as shown in attached photo?

or they have extracted/calculated wrong values of zeros and poles?

$$s_0=-\frac{1}{\tau}$$
$$s_{\infty}=-\frac{1}{\beta\tau}$$
because for $$s=s_0$$ the numerator becomes zero, and for $$s=s_{\infty}$$ the denominator becomes zero.