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