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I have an expression like this

(E^(-(j + k) y) (-1 + E^(i y)))/(j k)

I would like to take E^(i y) out of the brackets to get

(E^(i y + (-j - k) y) (1 - E^(-i y)))/(j k)

Of course, I can do such thing by copy and paste, but I wonder if there is a trick to do it programmatically.

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You can try the following:

factorOut[fac_][expr_] := Replace[expr, p_Plus :> fac Simplify[p/fac], All]

It is used as

factorOut[E^(i y)][(E^(-(j + k) y) (-1 + E^(i y)))/(j k)]
(* (E^(i y + (-j - k) y) (1 - E^(-i y)))/(j k) *)

$\frac{\left(1-e^{-i y}\right) e^{i y+y (-j-k)}}{j k}$

The idea is to try to pull out the specified factor from every sum. This is always correct as $p=f\cdot\frac pf$.The trick is that Mathematica doesn't revert this instantly since $\frac pf$ can be simplified.

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