\(A=\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10-5}\)
\(A=\frac{\left(2x+1\right)\left(2x+1\right)-\left(2x-1\right)\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}:\frac{4x}{10-5}\)
\(A=\frac{\left(2x+1\right)^2-\left(2x-1\right)^2}{\left(2x-1\right)\left(2x+1\right)}:\frac{4x}{10-5}\)
\(A=\frac{\left(2x\right)^2+2.2x+1-\left(2x\right)^2+2.2x-1}{\left(2x-1\right)\left(2x+1\right)}:\frac{4}{10-5}\)
\(A=\frac{\left(2x\right)^2+4x+1-\left(2x\right)^2+4x-1}{\left(2x-1\right)\left(2x+1\right)}:\frac{4x}{10-5}\)
\(A=\frac{\left[\left(2x\right)^2-\left(2x\right)^2\right]+\left(4x+4x\right)+\left(1-1\right)}{\left(2x-1\right)\left(2x+1\right)}:\frac{4x}{10-5}\)
\(A=\frac{8x}{\left(2x-1\right)\left(2x+1\right)}:\frac{4x}{10-5}\)
\(A=\frac{8x}{\left(2x-1\right)\left(2x+1\right)}:\frac{4x}{5}\)
\(A=\frac{8x}{\left(2x-1\right)\left(2x+1\right)}:\left(4x.5\right)\)
\(A=\frac{8x}{\left(2x-1\right)\left(2x+1\right)}:20x\)
\(A=\frac{8x}{20x\left(2x-1\right)\left(2x+1\right)}\)
\(A=\frac{8}{20\left(2x-1\right)\left(2x+1\right)}\)
\(A=\frac{2}{5\left(2x-1\right)\left(2x+1\right)}\)
