If I look at
Simplify[dglsolσ1[[1, 1, 2]][x]]
and I assume all your variables are likely Real and positive then there is a single term in your numerator containing -I*expression.
Unless in your maze of radicals and minus signs there are other lurking Complex values, it seems that you need to carefully look at that smaller expression and see whether you can recognize that it is in fact equal to zero. It doesn't appear that Mathematica can recognize that, not at least without additional information, and my attempts to help it with Assuming have failed.