\(A=\dfrac{2x+1}{4x-2}+\dfrac{1-2x}{4x+2}-\dfrac{2}{1-4x^2}\)
\(=\dfrac{2x+1}{2\left(2x-1\right)}+\dfrac{1-2x}{2\left(2x+1\right)}+\dfrac{2}{\left(2x-1\right)\left(2x+1\right)}\)\(=\dfrac{\left(2x+1\right)^2+\left(1-2x\right)^2+4}{2\left(2x-1\right)\left(2x+1\right)}\)
\(=\dfrac{4x^2+4x+1+1-4x+4x^2+4}{2\left(2x-1\right)\left(2x+1\right)}\)
\(=\dfrac{8x^2+6}{2\left(4x^2-1\right)}=\dfrac{8x^2-2+8}{8x^2-2}=1+\dfrac{8}{2\left(4x^2-1\right)}\)\(=1+\dfrac{4}{4x^2-1}\)
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