(i) Write \(\ln\left(\dfrac{2x+1}{2x-1}\right)\) as the difference of two logarithms.

A curve has equation \(y=\ln\left(\dfrac{2x+1}{2x-1}\right)+4x\), for \(x\gt \dfrac12\).

(ii) Using your answer to part (i), show that \(\dfrac{dy}{dx}=\dfrac{ax^2+b}{4x^2-1}\), where \(a\) and \(b\) are integers.

(iii) Hence find the \(x\)-coordinate of the stationary point on the curve.

(iv) Determine the nature of this stationary point.