Господин Экзамен
Общий знаменатель t^2/4*a+t-16*a^2/4*a+t
Решение
Вы ввели
[src]
2 2 t *a 16*a *a ---- + t - ------- + t 4 4
$$\frac{a t^{2}}{4} - \frac{16 a a^{2}}{4} + t + t$$
t^2*a/4 + t - 16*a^2*a/4 + t
Общее упрощение
[src]
2
3 a*t
- 4*a + 2*t + ----
4
$$- 4 a^{3} + \frac{a t^{2}}{4} + 2 t$$
-4*a^3 + 2*t + a*t^2/4
Разложение на множители
[src]
/ ________________________________ \ / ________________________________ \ / ________________________________ \ | / __________________ | | / __________________ | | / __________________ | | / / 6 2 | | / / 6 2 | | / / 6 2 | | / / 27*t 729*t | | / / 27*t 729*t | | / / 27*t 729*t | | / / - ----- + ------ | | / / - ----- + ------ / ___\ | | / / - ----- + ------ / ___\ | | / \/ 1024 4 27*t | | / \/ 1024 4 27*t | 1 I*\/ 3 | | | / \/ 1024 4 27*t | 1 I*\/ 3 | | | 3 / ----------------------- - ---- 2 | | 3 / ----------------------- - ---- *|- - - -------| 2 | | 3 / ----------------------- - ---- *|- - + -------| 2 | | \/ 2 4 t | | \/ 2 4 \ 2 2 / t | | \/ 2 4 \ 2 2 / t | 1*|a + ---------------------------------------- + -------------------------------------------|*|a + -------------------------------------------------------- + -----------------------------------------------------------|*|a + -------------------------------------------------------- + -----------------------------------------------------------| | 3 ________________________________| | 3 ________________________________| | 3 ________________________________| | / __________________ | | / __________________ | | / __________________ | | / / 6 2 | | / / 6 2 | | / / 6 2 | | / / 27*t 729*t | | / / 27*t 729*t | | / / 27*t 729*t | | / / - ----- + ------ | | / ___\ / / - ----- + ------ | | / ___\ / / - ----- + ------ | | / \/ 1024 4 27*t | | | 1 I*\/ 3 | / \/ 1024 4 27*t | | | 1 I*\/ 3 | / \/ 1024 4 27*t | | 16*3 / ----------------------- - ---- | | 16*|- - - -------|*3 / ----------------------- - ---- | | 16*|- - + -------|*3 / ----------------------- - ---- | \ \/ 2 4 / \ \ 2 2 / \/ 2 4 / \ \ 2 2 / \/ 2 4 /
$$1 \left(a + \left(\frac{t^{2}}{16 \sqrt[3]{- \frac{27 t}{4} + \frac{\sqrt{- \frac{27 t^{6}}{1024} + \frac{729 t^{2}}{4}}}{2}}} + \frac{\sqrt[3]{- \frac{27 t}{4} + \frac{\sqrt{- \frac{27 t^{6}}{1024} + \frac{729 t^{2}}{4}}}{2}}}{3}\right)\right) \left(a + \left(\frac{t^{2}}{16 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t}{4} + \frac{\sqrt{- \frac{27 t^{6}}{1024} + \frac{729 t^{2}}{4}}}{2}}} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t}{4} + \frac{\sqrt{- \frac{27 t^{6}}{1024} + \frac{729 t^{2}}{4}}}{2}}}{3}\right)\right) \left(a + \left(\frac{t^{2}}{16 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t}{4} + \frac{\sqrt{- \frac{27 t^{6}}{1024} + \frac{729 t^{2}}{4}}}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 t}{4} + \frac{\sqrt{- \frac{27 t^{6}}{1024} + \frac{729 t^{2}}{4}}}{2}}}{3}\right)\right)$$
((1*(a + ((sqrt(-27*t^6/1024 + 729*t^2/4)/2 - 27*t/4)^(1/3)/3 + t^2/(16*(sqrt(-27*t^6/1024 + 729*t^2/4)/2 - 27*t/4)^(1/3)))))*(a + ((sqrt(-27*t^6/1024 + 729*t^2/4)/2 - 27*t/4)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 + t^2/(16*(-1/2 - i*sqrt(3)/2)*(sqrt(-27*t^6/1024 + 729*t^2/4)/2 - 27*t/4)^(1/3)))))*(a + ((sqrt(-27*t^6/1024 + 729*t^2/4)/2 - 27*t/4)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 + t^2/(16*(-1/2 + i*sqrt(3)/2)*(sqrt(-27*t^6/1024 + 729*t^2/4)/2 - 27*t/4)^(1/3))))
Собрать выражение
[src]
2
3 a*t
- 4*a + 2*t + ----
4
$$- 4 a^{3} + \frac{a t^{2}}{4} + 2 t$$
-4*a^3 + 2*t + a*t^2/4
Рациональный знаменатель
[src]
2
3 a*t
- 4*a + 2*t + ----
4
$$- 4 a^{3} + \frac{a t^{2}}{4} + 2 t$$
3 2
- 16*a + 8*t + a*t
--------------------
4
$$\frac{- 16 a^{3} + a t^{2} + 8 t}{4}$$
(-16*a^3 + 8*t + a*t^2)/4
Общий знаменатель
[src]
2
3 a*t
- 4*a + 2*t + ----
4
$$- 4 a^{3} + \frac{a t^{2}}{4} + 2 t$$
-4*a^3 + 2*t + a*t^2/4
Степени
[src]
2
3 a*t
- 4*a + 2*t + ----
4
$$- 4 a^{3} + \frac{a t^{2}}{4} + 2 t$$
-4*a^3 + 2*t + a*t^2/4
Комбинаторика
[src]
2
3 a*t
- 4*a + 2*t + ----
4
$$- 4 a^{3} + \frac{a t^{2}}{4} + 2 t$$
-4*a^3 + 2*t + a*t^2/4
Объединение рациональных выражений
[src]
3 2
- 16*a + 8*t + a*t
--------------------
4
$$\frac{- 16 a^{3} + a t^{2} + 8 t}{4}$$
(-16*a^3 + 8*t + a*t^2)/4