`[4x^2+2x]/[4x^2-1]=[2x(2x+1)]/[(2x-1)(2x+1)]=[2x]/[2x-1]`
`=>A=2x`
`->bb D`
\(\dfrac{4x^2+2x}{4x^2-1}=\dfrac{A}{2x-1}\\ =>\dfrac{2x\left(2x+1\right)}{\left(2x+1\right)\left(2x-1\right)}=\dfrac{A}{2x-1}\\ =>\dfrac{2x}{2x-1}=\dfrac{A}{2x-1}\\ =>A=2x\)