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Try:

sage: var("t, tau, tau_1, tau_2")
(t, tau, tau_1, tau_2)
sage: f = tau_1*exp(-t/tau_1)/(tau_1 - tau_2) - tau_1*exp(-t/tau_2)/(tau_1-tau_2)
....: 
sage: f.collect_common_factors()
tau_1*(e^(-t/tau_1) - e^(-t/tau_2))/(tau_1 - tau_2)

(i. e. $\frac{\tau_{1} {\left(e^{\left(-\frac{t}{\tau_{1}}\right)} - e^{\left(-\frac{t}{\tau_{2}}\right)}\right)}}{\tau_{1} - \tau_{2}}$), which, IMHO, is what you seek.