Description of the quasy-steady-state approximation method is done in the section "Quasi-Steady-State Analysis". Below we use the notation given there.
As an example consider the simplest enzyme reaction
which involves an enzyme E binding to a substrate S to form a complex ES and its dissociation into a product P and the enzyme E.
Let us find the conditions under which the concentration of the complex ES is quasi-stationary in time t = 0. To do this, we consider the expressions
which result in the following derivatives
Next, we find the formulas for δtES and rES:
Thus, the complex ES is in quasi-steady state at t = 0 only when δtES << 1, i.e.