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