More intuitve way to simplify a simple expression involving two exponential factors

Question

Is there a way to ask Mathematica to simplify expressions it generates, like:

$e^{-\frac{A t}{v^3}-\frac{v^2}{2 w^2}} \left(-1+e^{\frac{A t}{v^3}}\right)$

into a more readable form by taking out the common factor, like:

$e^{-\frac{v^2}{2 w^2}} \left(1-e^{-\frac{A t}{v^3}}\right)$

Here is the Mma code to simplify the first equation:

Simplify[E^(-((A t)/v^3) - v^2/(2 w^2)) (-1 + E^((A t)/v^3))]

Please include Mathematica code that can be copied, pasted, executed and therefore amenable to study in our own notebook sessions. Thanks. — Syed, Dec 02 '23 at 04:18
E^(-((A t)/v^3) - v^2/(2 w^2)) (-1 + E^((A t)/v^3)) // Expand // Collect[#, Exp[-v^2/2/w^2]] & — chris, Dec 02 '23 at 05:16

score 2 · Accepted Answer · answered Dec 02 '23 at 06:39

into a more readable form by taking out the common factor, like:

$e^{-\frac{v^2}{2 w^2}} \left(1-e^{-\frac{A t}{v^3}}\right)$

You could try

ClearAll["Global`*"]
expr = E^(-((A t)/v^3) - v^2/(2 w^2)) (-1 + E^((A t)/v^3))
expr /. Exp[a_ + b_]*c_ :> Exp[b]*Simplify[Exp[a]*c]

Mathematica graphics

But this might not work for all cases because the main problem is that Mathematica likes to write $e^a e^b$ as $e^{a+b}$ by default. See How to tell Mathematica to avoid simplification of product of exponentials with the same base? and other links in it for more discussion on this.

1 Answers1