2 2*(2*x + 1)
------- - -----------
2*x - 1 2
(2*x - 1)
---------------------
2
(2*x + 1)
1 + ----------
2
(2*x - 1)
$$\frac{\frac{2}{2 x - 1} - \frac{2 \left(2 x + 1\right)}{\left(2 x - 1\right)^{2}}}{1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}}$$
/ / 1 + 2*x \ \
| (1 + 2*x)*|1 - --------| |
/ 1 + 2*x \ | \ -1 + 2*x/ |
-8*|1 - --------|*|1 + ----------------------------|
\ -1 + 2*x/ | / 2\ |
| | (1 + 2*x) | |
| |1 + -----------|*(-1 + 2*x)|
| | 2| |
\ \ (-1 + 2*x) / /
----------------------------------------------------
/ 2\
| (1 + 2*x) | 2
|1 + -----------|*(-1 + 2*x)
| 2|
\ (-1 + 2*x) /
$$- \frac{8 \left(1 - \frac{2 x + 1}{2 x - 1}\right) \left(1 + \frac{\left(1 - \frac{2 x + 1}{2 x - 1}\right) \left(2 x + 1\right)}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right) \left(2 x - 1\right)}\right)}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right) \left(2 x - 1\right)^{2}}$$
/ 2 \
| 4*(1 + 2*x) 3*(1 + 2*x) 2 |
| 1 - ----------- + ------------ 2 / 1 + 2*x \ / 1 + 2*x \ |
| -1 + 2*x 2 4*(1 + 2*x) *|1 - --------| 4*(1 + 2*x)*|1 - --------| |
/ 1 + 2*x \ | (-1 + 2*x) \ -1 + 2*x/ \ -1 + 2*x/ |
16*|1 - --------|*|3 - ------------------------------ + ------------------------------ + ----------------------------|
\ -1 + 2*x/ | 2 2 / 2\ |
| (1 + 2*x) / 2\ | (1 + 2*x) | |
| 1 + ----------- | (1 + 2*x) | 2 |1 + -----------|*(-1 + 2*x)|
| 2 |1 + -----------| *(-1 + 2*x) | 2| |
| (-1 + 2*x) | 2| \ (-1 + 2*x) / |
\ \ (-1 + 2*x) / /
----------------------------------------------------------------------------------------------------------------------
/ 2\
| (1 + 2*x) | 3
|1 + -----------|*(-1 + 2*x)
| 2|
\ (-1 + 2*x) /
$$\frac{16 \left(1 - \frac{2 x + 1}{2 x - 1}\right) \left(3 + \frac{4 \left(1 - \frac{2 x + 1}{2 x - 1}\right) \left(2 x + 1\right)}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right) \left(2 x - 1\right)} - \frac{1 - \frac{4 \left(2 x + 1\right)}{2 x - 1} + \frac{3 \left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}}{1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}} + \frac{4 \left(1 - \frac{2 x + 1}{2 x - 1}\right)^{2} \left(2 x + 1\right)^{2}}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right)^{2} \left(2 x - 1\right)^{2}}\right)}{\left(1 + \frac{\left(2 x + 1\right)^{2}}{\left(2 x - 1\right)^{2}}\right) \left(2 x - 1\right)^{3}}$$