# Excluding a common factor in a sum

I'm trying to figure out how to simplify this expression in Sage:

y = tau1*exp(-t/tau1)/(tau1 - tau2) - tau1*exp(-t/tau2)/(tau1-tau2)


When I try factor(y) or simplify(y), I get this:

-tau1*(e^(t/tau1) - e^(t/tau2))*e^(-t/tau1 - t/tau2)/(tau1 - tau2)


However, the result I would like to see is this:

 tau1/(tau1 - tau2)*(exp(-t/tau1) - exp(-t/tau2))


which seems like the simplest form to me. I've not been able to get this result with the various simplify commands or with assumptions (BTW, all variables are real, and tau1 & tau2 > 0).

In this case the simplest form is obvious, of course, but it would be a great help to be able to get this right for larger expressions.

edit retag close merge delete

Sort by » oldest newest most voted

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.

more