Господин Экзамен
Общий знаменатель (x^17)/(1-x^15)-(1-x^15)/(x^13-1)
Решение
Вы ввели
[src]
17 15
x 1 - x
------- - -------
15 13
1 - x x - 1
$$\frac{x^{17}}{- x^{15} + 1} - \frac{- x^{15} + 1}{x^{13} - 1}$$
x^17/(1 - x^15) - (1 - x^15)/(x^13 - 1*1)
Общее упрощение
[src]
2 / 15\ 17 / 13\ \-1 + x / + x *\1 - x / --------------------------- / 13\ / 15\ \-1 + x /*\-1 + x /
$$\frac{x^{17} \cdot \left(- x^{13} + 1\right) + \left(x^{15} - 1\right)^{2}}{\left(x^{13} - 1\right) \left(x^{15} - 1\right)}$$
((-1 + x^15)^2 + x^17*(1 - x^13))/((-1 + x^13)*(-1 + x^15))
Разложение дроби
[src]
-1/(15*(-1 + x)) + (1 + x)/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12) - (1 + 2*x)/(15*(1 + x + x^2)) + (1 - 6*x^3 - 3*x^6 + 2*x^7 + 5*x^5 + 7*x^2)/(15*(1 + x^3 + x^5 + x^8 - x - x^4 - x^7)) + (-1 + x)*(1 + x^2 + 3*x)/(15*(1 + x + x^2 + x^3 + x^4))
$$\frac{\left(x - 1\right) \left(x^{2} + 3 x + 1\right)}{15 \left(x^{4} + x^{3} + x^{2} + x + 1\right)} + \frac{x + 1}{x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1} - \frac{2 x + 1}{15 \left(x^{2} + x + 1\right)} + \frac{2 x^{7} - 3 x^{6} + 5 x^{5} - 6 x^{3} + 7 x^{2} + 1}{15 \left(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\right)} - \frac{1}{15 \left(x - 1\right)}$$
3 6 7 5 2 / 2 \
1 1 + x 1 + 2*x 1 - 6*x - 3*x + 2*x + 5*x + 7*x (-1 + x)*\1 + x + 3*x/
- ----------- + --------------------------------------------------------------- - --------------- + ------------------------------------ + -------------------------
15*(-1 + x) 2 3 4 5 6 7 8 9 10 11 12 / 2\ / 3 5 8 4 7\ / 2 3 4\
1 + x + x + x + x + x + x + x + x + x + x + x + x 15*\1 + x + x / 15*\1 + x + x + x - x - x - x / 15*\1 + x + x + x + x /
Объединение рациональных выражений
[src]
2
/ 15\ 17 / 13\
- \1 - x / + x *\-1 + x /
-----------------------------
/ 15\ / 13\
\1 - x /*\-1 + x /
$$\frac{x^{17} \left(x^{13} - 1\right) - \left(- x^{15} + 1\right)^{2}}{\left(- x^{15} + 1\right) \left(x^{13} - 1\right)}$$
(-(1 - x^15)^2 + x^17*(-1 + x^13))/((1 - x^15)*(-1 + x^13))
Численный ответ
[src]
x^17/(1.0 - x^15) - (1.0 - x^15)/(-1.0 + x^13)
x^17/(1.0 - x^15) - (1.0 - x^15)/(-1.0 + x^13)
Рациональный знаменатель
[src]
15 17
1 x x
- -------- + -------- + -------
13 13 15
-1 + x -1 + x 1 - x
$$\frac{x^{17}}{- x^{15} + 1} + \frac{x^{15}}{x^{13} - 1} - \frac{1}{x^{13} - 1}$$
17 / 13\ / 15\ / 15\
x *\-1 + x / + \1 - x /*\-1 + x /
-------------------------------------
/ 15\ / 13\
\1 - x /*\-1 + x /
$$\frac{x^{17} \left(x^{13} - 1\right) + \left(- x^{15} + 1\right) \left(x^{15} - 1\right)}{\left(- x^{15} + 1\right) \left(x^{13} - 1\right)}$$
(x^17*(-1 + x^13) + (1 - x^15)*(-1 + x^15))/((1 - x^15)*(-1 + x^13))
Общий знаменатель
[src]
15 16 2 3 4 5 6 7 8 9 10 11 12 13 14
-1 + x + x - x - x - x - x - x - x - x - x - x - x - x - x - x - x
----------------------------------------------------------------------------------------------------------------------------------------------
15 16 17 18 19 20 21 22 23 24 25 26 27 2 3 4 5 6 7 8 9 10 11 12
-1 + x + x + x + x + x + x + x + x + x + x + x + x + x - x - x - x - x - x - x - x - x - x - x - x - x
$$\frac{x^{16} + x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1}{x^{27} + x^{26} + x^{25} + x^{24} + x^{23} + x^{22} + x^{21} + x^{20} + x^{19} + x^{18} + x^{17} + x^{16} + x^{15} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1}$$
(-1 + x^15 + x^16 - x - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9 - x^10 - x^11 - x^12 - x^13 - x^14)/(-1 + x^15 + x^16 + x^17 + x^18 + x^19 + x^20 + x^21 + x^22 + x^23 + x^24 + x^25 + x^26 + x^27 - x - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9 - x^10 - x^11 - x^12)
Степени
[src]
17 15
x -1 + x
------- + --------
15 13
1 - x -1 + x
$$\frac{x^{17}}{- x^{15} + 1} + \frac{x^{15} - 1}{x^{13} - 1}$$
17 15
x -1 + x
------- + --------
15 13
1 - x x - 1
$$\frac{x^{17}}{- x^{15} + 1} + \frac{x^{15} - 1}{x^{13} - 1}$$
x^17/(1 - x^15) + (-1 + x^15)/(x^13 - 1*1)
Комбинаторика
[src]
15 16 2 3 4 5 6 7 8 9 10 11 12 13 14
-1 + x + x - x - x - x - x - x - x - x - x - x - x - x - x - x - x
-----------------------------------------------------------------------------------------------------------------------------------------------
/ 2\ / 2 3 4\ / 3 5 8 4 7\ / 2 3 4 5 6 7 8 9 10 11 12\
(-1 + x)*\1 + x + x /*\1 + x + x + x + x /*\1 + x + x + x - x - x - x /*\1 + x + x + x + x + x + x + x + x + x + x + x + x /
$$\frac{x^{16} + x^{15} - x^{14} - x^{13} - x^{12} - x^{11} - x^{10} - x^{9} - x^{8} - x^{7} - x^{6} - x^{5} - x^{4} - x^{3} - x^{2} - x - 1}{\left(x - 1\right) \left(x^{2} + x + 1\right) \left(x^{4} + x^{3} + x^{2} + x + 1\right) \left(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\right) \left(x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1\right)}$$
(-1 + x^15 + x^16 - x - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9 - x^10 - x^11 - x^12 - x^13 - x^14)/((-1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 + x^3 + x^5 + x^8 - x - x^4 - x^7)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12))