Господин Экзамен
Общий знаменатель a^2/3-3*a^3/2-3
Решение
Вы ввели
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2 3 a 3*a -- - ---- - 3 3 2
$$- \frac{3 a^{3}}{2} + \frac{a^{2}}{3} - 3$$
a^2/3 - 3*a^3/2 - 1*3
Разложение дроби
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-3 - 3*a^3/2 + a^2/3
$$- \frac{3 a^{3}}{2} + \frac{a^{2}}{3} - 3$$
3 2
3*a a
-3 - ---- + --
2 3
Разложение на множители
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/ ___________________ \ / ___________________ \ / ___________________\ | / _______ / ___\| | / _______ / ___\| | / _______ | | / 19675 \/ 59001 | 1 I*\/ 3 || | / 19675 \/ 59001 | 1 I*\/ 3 || | / 19675 \/ 59001 | | 3 / ----- + --------- *|- - - -------|| | 3 / ----- + --------- *|- - + -------|| | 3 / ----- + --------- | | 2 4 \/ 729 9 \ 2 2 /| | 2 4 \/ 729 9 \ 2 2 /| | 2 4 \/ 729 9 | 1*|a + - -- + -------------------------------------------- + ----------------------------------------|*|a + - -- + -------------------------------------------- + ----------------------------------------|*|a + - -- + ---------------------------- + ------------------------| | 27 ___________________ 3 | | 27 ___________________ 3 | | 27 ___________________ 3 | | / ___\ / _______ | | / ___\ / _______ | | / _______ | | | 1 I*\/ 3 | / 19675 \/ 59001 | | | 1 I*\/ 3 | / 19675 \/ 59001 | | / 19675 \/ 59001 | | 243*|- - - -------|*3 / ----- + --------- | | 243*|- - + -------|*3 / ----- + --------- | | 243*3 / ----- + --------- | \ \ 2 2 / \/ 729 9 / \ \ 2 2 / \/ 729 9 / \ \/ 729 9 /
$$1 \left(a + \left(- \frac{2}{27} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{59001}}{9} + \frac{19675}{729}}}{3} + \frac{4}{243 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{59001}}{9} + \frac{19675}{729}}}\right)\right) \left(a + \left(- \frac{2}{27} + \frac{4}{243 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{59001}}{9} + \frac{19675}{729}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{59001}}{9} + \frac{19675}{729}}}{3}\right)\right) \left(a + \left(- \frac{2}{27} + \frac{4}{243 \sqrt[3]{\frac{\sqrt{59001}}{9} + \frac{19675}{729}}} + \frac{\sqrt[3]{\frac{\sqrt{59001}}{9} + \frac{19675}{729}}}{3}\right)\right)$$
((1*(a - (2/27 + 4/(243*(-1/2 - i*sqrt(3)/2)*(19675/729 + sqrt(59001)/9)^(1/3)) + (19675/729 + sqrt(59001)/9)^(1/3)*(-1/2 - i*sqrt(3)/2)/3)))*(a - (2/27 + 4/(243*(-1/2 + i*sqrt(3)/2)*(19675/729 + sqrt(59001)/9)^(1/3)) + (19675/729 + sqrt(59001)/9)^(1/3)*(-1/2 + i*sqrt(3)/2)/3)))*(a - (2/27 + 4/(243*(19675/729 + sqrt(59001)/9)^(1/3)) + (19675/729 + sqrt(59001)/9)^(1/3)/3))
Объединение рациональных выражений
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3 2
-18 - 9*a + 2*a
-----------------
6
$$\frac{- 9 a^{3} + 2 a^{2} - 18}{6}$$
(-18 - 9*a^3 + 2*a^2)/6
Рациональный знаменатель
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3 2
-18 - 9*a + 2*a
-----------------
6
$$\frac{- 9 a^{3} + 2 a^{2} - 18}{6}$$
(-18 - 9*a^3 + 2*a^2)/6