(2 z (2 z + 1))/(2 z - 1)^3
(4 z^2)/(8 z^3 - 12 z^2 + 6 z - 1) + (2 z)/(8 z^3 - 12 z^2 + 6 z - 1)
(4 z^2 + 2 z)/(8 z^3 - 12 z^2 + 6 z - 1)
(4 z^2)/(2 z - 1)^3 + (2 z)/(2 z - 1)^3
1/(2 z - 1) + 3/(2 z - 1)^2 + 2/(2 z - 1)^3
(z (4 z + 2))/(z (z (8 z - 12) + 6) - 1)