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