Let \( f:\mathbb{R}-\left\{\displaystyle\,\frac{-1}{2}\,\right\}\to \mathbb{R} \) and \( g:\mathbb{R}-\left\{\displaystyle\,\frac{-5}{2}\,\right\}\to \mathbb{R} \) be defined as \(\displaystyle f(x)=\frac{2x+3}{2x+1} \) and \(\displaystyle g(x)=\frac{|x|+1}{2x+5} \). Then, the domain of the function fog is:
