Rational approximations of the exponential function at rational points

We give explicit and asymptotic lower bounds for the quantity $\mathrm{\mid }{e}^{s\mathrm{/}t}-M\mathrm{/}N\mathrm{\mid }$ by studying a generalized continued fraction expansion of $e^{s\mathrm{/}t}$. In cases $\mathrm{\mid }s\mathrm{\mid }\ge 3$ we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction.