\(\dfrac{4x^2+4x+1}{4x^2-1}-\dfrac{2}{2x-1}-3\)
\(=\dfrac{\left(2x+1\right)^2}{\left(2x-1\right)\left(2x+1\right)}-\dfrac{2}{2x-1}-3\)
\(=\dfrac{2x+1}{2x-1}-\dfrac{2}{2x-1}-\dfrac{3\left(2x-1\right)}{2x-1}\)
\(=\dfrac{2x+1-2-6x+3}{2x-1}\)
\(=\dfrac{-4x+2}{2x-1}\)
\(=\dfrac{-2\left(2x-1\right)}{2x-1}=-2\)