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I wanna make global assumptions

 $Assumptions = A \[Element] Reals && B \[Element] Reals 

Then I wanna simplify

 FullSimplify[Re[1/(A + B)]]

I get output

 Re[1/(A + B)]

I wanna get output

 1/(A + B)

What is the problem?

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    $\begingroup$ Learn about ComplexExpand; that's what you are probably looking for... $\endgroup$ – Henrik Schumacher Jan 12 '18 at 16:12
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    $\begingroup$ Add the assumption A + B != 0? Sometimes the transformations used by Simplify balk if the result could be nonnumeric, or so it seems to me. $\endgroup$ – Michael E2 Jan 12 '18 at 16:45
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Adding the assumption A + B != 0 works with FullSimplify, too:

Simplify[Re[1/(A + B)], A ∈ Reals && B ∈ Reals && A + B != 0]

(*  1/(A + B)  *)

Sometimes the transformations used by Simplify and FullSimplify balk if the result could be nonnumeric, or so it seems to me.

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