3/2 2 3/2 ___
b + 3*a - 3*a *\/ b + 3*a*b
----------------------------------
___
\/ a
$$\frac{- 3 a^{\frac{3}{2}} \sqrt{b} + b^{\frac{3}{2}} + 3 a^{2} + 3 a b}{\sqrt{a}}$$
(b^(3/2) + 3*a^2 - 3*a^(3/2)*sqrt(b) + 3*a*b)/sqrt(a)
Подстановка условия
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(sqrt(a) - sqrt(b))^3 + 2*a^2/(sqrt(a)) + b*sqrt(b)*sqrt(a)/a + b*sqrt(b) при a = -3
3 2 ___ ___
/ ___ ___\ 2*a b*\/ b *\/ a ___
\\/ a - \/ b / + ----- + ------------- + b*\/ b
___ a
\/ a
$$\left(\sqrt{a} - \sqrt{b}\right)^{3} + \frac{\sqrt{a} \sqrt{b} b}{a} + \sqrt{b} b + \frac{2 a^{2}}{\sqrt{a}}$$
3/2 2 3/2 ___
b + 3*a - 3*a *\/ b + 3*a*b
----------------------------------
___
\/ a
$$\frac{- 3 a^{\frac{3}{2}} \sqrt{b} + b^{\frac{3}{2}} + 3 a^{2} + 3 a b}{\sqrt{a}}$$
$$a = -3$$
3/2 2 3/2 ___
b + 3*(-3) - 3*(-3) *\/ b + 3*(-3)*b
-------------------------------------------
______
\/ (-3)
$$\frac{- 3 (-3)^{\frac{3}{2}} \sqrt{b} + b^{\frac{3}{2}} + 3 (-3)^{2} + 3 (-3) b}{\sqrt{(-3)}}$$
3/2 2 3/2 ___
b + 3*(-3) - 3*(-3) *\/ b + 3*-3*b
-----------------------------------------
____
\/ -3
$$\frac{b^{\frac{3}{2}} - 3 \left(-3\right)^{\frac{3}{2}} \sqrt{b} + 3 \left(-3\right) b + 3 \left(-3\right)^{2}}{\sqrt{3} i}$$
___ / 3/2 ___ ___\
-I*\/ 3 *\27 + b - 9*b + 9*I*\/ 3 *\/ b /
---------------------------------------------
3
$$- \frac{\sqrt{3} i \left(b^{\frac{3}{2}} + 9 \sqrt{3} i \sqrt{b} - 9 b + 27\right)}{3}$$
-i*sqrt(3)*(27 + b^(3/2) - 9*b + 9*i*sqrt(3)*sqrt(b))/3
3 3/2
3/2 / ___ ___\ 3/2 b
b + \\/ a - \/ b / + 2*a + -----
___
\/ a
$$2 a^{\frac{3}{2}} + b^{\frac{3}{2}} + \left(\sqrt{a} - \sqrt{b}\right)^{3} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}$$
3
/ ___ ___\ 3/2 3/2 / 1 \
\\/ a - \/ b / + 2*a + b *|1 + -----|
| ___|
\ \/ a /
$$b^{\frac{3}{2}} \cdot \left(1 + \frac{1}{\sqrt{a}}\right) + 2 a^{\frac{3}{2}} + \left(\sqrt{a} - \sqrt{b}\right)^{3}$$
(sqrt(a) - sqrt(b))^3 + 2*a^(3/2) + b^(3/2)*(1 + 1/sqrt(a))
3/2 2
b + 3*a + 3*a*b ___
------------------- - 3*a*\/ b
___
\/ a
$$- 3 a \sqrt{b} + \frac{b^{\frac{3}{2}} + 3 a^{2} + 3 a b}{\sqrt{a}}$$
(b^(3/2) + 3*a^2 + 3*a*b)/sqrt(a) - 3*a*sqrt(b)
Рациональный знаменатель
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3 3/2
3/2 / ___ ___\ 3/2 b
b + \\/ a - \/ b / + 2*a + -----
___
\/ a
$$2 a^{\frac{3}{2}} + b^{\frac{3}{2}} + \left(\sqrt{a} - \sqrt{b}\right)^{3} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}$$
____ ____ ____ ____ 3
3 / 3 3/2 / 3 3/2 3/2 / 3 3/2 / 3 / ___ ___\
2*a *\/ a + a*b *\/ a + a *b *\/ a + a *\/ a *\\/ a - \/ b /
---------------------------------------------------------------------------------
3
a
$$\frac{a^{\frac{3}{2}} b^{\frac{3}{2}} \sqrt{a^{3}} + a^{\frac{3}{2}} \left(\sqrt{a} - \sqrt{b}\right)^{3} \sqrt{a^{3}} + a b^{\frac{3}{2}} \sqrt{a^{3}} + 2 a^{3} \sqrt{a^{3}}}{a^{3}}$$
(2*a^3*sqrt(a^3) + a*b^(3/2)*sqrt(a^3) + a^(3/2)*b^(3/2)*sqrt(a^3) + a^(3/2)*sqrt(a^3)*(sqrt(a) - sqrt(b))^3)/a^3
3/2 2 3/2 ___
b + 3*a - 3*a *\/ b + 3*a*b
----------------------------------
___
\/ a
$$\frac{- 3 a^{\frac{3}{2}} \sqrt{b} + b^{\frac{3}{2}} + 3 a^{2} + 3 a b}{\sqrt{a}}$$
(b^(3/2) + 3*a^2 - 3*a^(3/2)*sqrt(b) + 3*a*b)/sqrt(a)
Объединение рациональных выражений
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3
3/2 2 ___ 3/2 ___ / ___ ___\
b + 2*a + \/ a *b + \/ a *\\/ a - \/ b /
-------------------------------------------------
___
\/ a
$$\frac{\sqrt{a} b^{\frac{3}{2}} + \sqrt{a} \left(\sqrt{a} - \sqrt{b}\right)^{3} + b^{\frac{3}{2}} + 2 a^{2}}{\sqrt{a}}$$
(b^(3/2) + 2*a^2 + sqrt(a)*b^(3/2) + sqrt(a)*(sqrt(a) - sqrt(b))^3)/sqrt(a)
3 3/2
3/2 / ___ ___\ 3/2 b
b + \\/ a - \/ b / + 2*a + -----
___
\/ a
$$2 a^{\frac{3}{2}} + b^{\frac{3}{2}} + \left(\sqrt{a} - \sqrt{b}\right)^{3} + \frac{b^{\frac{3}{2}}}{\sqrt{a}}$$
b^(3/2) + (sqrt(a) - sqrt(b))^3 + 2*a^(3/2) + b^(3/2)/sqrt(a)