________
/ 3 / 2 2 / 3\\
/ 1 + x / 3\ | x x *\1 + x /|
/ ------ *\1 - x /*|------ + -----------|
3 / 3 | 3 2 |
\/ 1 - x |1 - x / 3\ |
\ \1 - x / /
----------------------------------------------
3
1 + x
$$\frac{\sqrt[3]{\frac{x^{3} + 1}{- x^{3} + 1}}}{x^{3} + 1} \left(- x^{3} + 1\right) \left(\frac{x^{2}}{- x^{3} + 1} + \frac{x^{2} \left(x^{3} + 1\right)}{\left(- x^{3} + 1\right)^{2}}\right)$$
((1.0 + x^3)/(1.0 - x^3))^0.333333333333333*(1.0 - x^3)*(x^2/(1.0 - x^3) + x^2*(1.0 + x^3)/(1.0 - x^3)^2)/(1.0 + x^3)
Рациональный знаменатель
[src] ________
/ 3 / 2 \
/ 1 + x | 2 / 3\ 2 / 3\ / 3\|
/ ------ *\x *\1 - x / + x *\1 + x /*\1 - x //
3 / 3
\/ 1 - x
----------------------------------------------------
2
/ 3\ / 3\
\1 + x /*\1 - x /
$$\frac{\sqrt[3]{\frac{x^{3} + 1}{- x^{3} + 1}}}{\left(- x^{3} + 1\right)^{2} \left(x^{3} + 1\right)} \left(x^{2} \left(- x^{3} + 1\right)^{2} + x^{2} \left(- x^{3} + 1\right) \left(x^{3} + 1\right)\right)$$
Объединение рациональных выражений
[src] ________
/ 3
2 / 1 + x
2*x * / ------
3 / 3
\/ 1 - x
-------------------
/ 3\ / 3\
\1 + x /*\1 - x /
$$\frac{2 x^{2} \sqrt[3]{\frac{x^{3} + 1}{- x^{3} + 1}}}{\left(- x^{3} + 1\right) \left(x^{3} + 1\right)}$$
____________
/ / 3\
2 / -\1 + x /
-2*x * / ----------
3 / 3
\/ -1 + x
------------------------
6
-1 + x
$$- \frac{2 x^{2}}{x^{6} - 1} \sqrt[3]{- \frac{x^{3} + 1}{x^{3} - 1}}$$
________
/ 3 / 2 2 / 3\\
/ 1 + x / 3\ | x x *\1 + x /|
/ ------ *\1 - x /*|------ + -----------|
3 / 3 | 3 2 |
\/ 1 - x |1 - x / 3\ |
\ \1 - x / /
----------------------------------------------
3
1 + x
$$\frac{\sqrt[3]{\frac{x^{3} + 1}{- x^{3} + 1}}}{x^{3} + 1} \left(- x^{3} + 1\right) \left(\frac{x^{2}}{- x^{3} + 1} + \frac{x^{2} \left(x^{3} + 1\right)}{\left(- x^{3} + 1\right)^{2}}\right)$$
______________________
/ / 2 \
2 / (1 + x)*\1 + x - x/
-2*x * / --------------------
3 / 3
\/ 1 - x
------------------------------------------
/ 2\ / 2 \
(1 + x)*(-1 + x)*\1 + x + x /*\1 + x - x/
$$- \frac{2 x^{2} \sqrt[3]{\frac{\left(x + 1\right) \left(x^{2} - x + 1\right)}{- x^{3} + 1}}}{\left(x - 1\right) \left(x + 1\right) \left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)}$$
_________________
/ 3
2 / 1 x
-2*x * / ------ + ------
3 / 3 3
\/ 1 - x 1 - x
-----------------------------
6
-1 + x
$$- \frac{2 x^{2}}{x^{6} - 1} \sqrt[3]{\frac{x^{3}}{- x^{3} + 1} + \frac{1}{- x^{3} + 1}}$$
________ / 2 2 / 3\\
/ 1 / 3\ | x x *\1 + x /|
/ ------ *\1 - x /*|------ + -----------|
3 / 3 | 3 2 |
\/ 1 - x |1 - x / 3\ |
\ \1 - x / /
---------------------------------------------
2/3
/ 3\
\1 + x /
$$\frac{\sqrt[3]{\frac{1}{- x^{3} + 1}}}{\left(x^{3} + 1\right)^{\frac{2}{3}}} \left(- x^{3} + 1\right) \left(\frac{x^{2}}{- x^{3} + 1} + \frac{x^{2} \left(x^{3} + 1\right)}{\left(- x^{3} + 1\right)^{2}}\right)$$
________
/ 3 / 2 2 / 3\\
/ 1 + x / 3\ | x x *\1 + x /|
/ ------ *\1 - x /*|------ + -----------|
3 / 3 | 3 2 |
\/ 1 - x |1 - x / 3\ |
\ \1 - x / /
----------------------------------------------
3
1 + x
$$\frac{\sqrt[3]{\frac{x^{3} + 1}{- x^{3} + 1}}}{x^{3} + 1} \left(- x^{3} + 1\right) \left(\frac{x^{2}}{- x^{3} + 1} + \frac{x^{2} \left(x^{3} + 1\right)}{\left(- x^{3} + 1\right)^{2}}\right)$$