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exp(x/(x+1)+1/(x+1)) fails to be simplified

I have tried simplify and simplify_full on exp(x/(x+1)+1/(x+1)), expecting e as the result, but sage does not simplify it. Curiously, simplify_full works on log(x/(x+1)+1/(x+1)), and returns 0. Also (x/(x+1)+1/(x+1)).simplify_full() returns 1. By the way, this is just the simplest example I could come up with, originally I have noticed in much more complicated expressions that sage failed to simplify them, because it failed to simplify inside the exponents.