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