\(a,A=\dfrac{4x-2+4x^2+1+2x+1}{\left(2x-1\right)\left(2x+1\right)}\cdot\dfrac{\left(2x-1\right)\left(2x+1\right)}{2}\\ A=\dfrac{4x^2+6x}{2}=2x^2+3x\\ b,A=2\Leftrightarrow2x^2+3x-2=0\\ \Leftrightarrow2x^2+4x-x-2=0\\ \Leftrightarrow2x\left(x+2\right)-\left(x+2\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(x+2\right)=0\\ \Leftrightarrow x=-2\left(x\ne\dfrac{1}{2}\right)\)
\(c,A=2x^2+3x=2\left(x^2+2\cdot\dfrac{3}{4}x+\dfrac{9}{16}\right)-\dfrac{9}{8}=2\left(x+\dfrac{3}{4}\right)^2-\dfrac{9}{8}\ge-\dfrac{9}{8}\\ A_{min}=-\dfrac{9}{8}\Leftrightarrow x=-\dfrac{3}{4}\)
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