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