In their analysis, Michaelis and Menten (and also Henri) assumed that the substrate is in instantaneous chemical equilibrium with the complex, which implies
in which e is the concentration of free enzyme (not the total concentration) and x is the concentration of enzyme-substrate complex EA.
Conservation of enzyme requires that
where  is now the total enzyme concentration. After combining the two expressions some straightforward algebra leads to the following expression for the concentration of the enzyme-substrate complex:
where  is the dissociation constant of the enzyme-substrate complex. Hence the rate equation is the Michaelis–Menten equation,
where  corresponds to the catalytic constant  and the limiting rate is . Likewise with the assumption of equilibrium the Michaelis constant .