/ _____\ / 3/2 3/2 / _____\\
\a + b + 2*\/ a*b /*\a - b + a*\b + \/ a*b //
---------------------------------------------------
a*(a - b)
$$\frac{\left(a + b + 2 \sqrt{a b}\right) \left(a^{\frac{3}{2}} - b^{\frac{3}{2}} + a \left(b + \sqrt{a b}\right)\right)}{a \left(a - b\right)}$$
(a + b + 2*sqrt(a*b))*(a^(3/2) - b^(3/2) + a*(b + sqrt(a*b)))/(a*(a - b))
(a + b + 2.0*(a*b)^0.5)*(b + (a*b)^0.5 + (a^1.5 - b^1.5)/a)/(a - b)
(a + b + 2.0*(a*b)^0.5)*(b + (a*b)^0.5 + (a^1.5 - b^1.5)/a)/(a - b)
Рациональный знаменатель
[src]
/ _____\ / 3/2 3/2 / _____\\
\a + b + 2*\/ a*b /*\a - b + a*\b + \/ a*b //
---------------------------------------------------
a*(a - b)
$$\frac{\left(a + b + 2 \sqrt{a b}\right) \left(a^{\frac{3}{2}} - b^{\frac{3}{2}} + a \left(b + \sqrt{a b}\right)\right)}{a \left(a - b\right)}$$
3/2 2 3/2 5/2 _____ ___ 3/2 _____ ___ _____ _____
a b b b a*\/ a*b b*\/ a 2*b *\/ a*b 2*\/ a *\/ a*b 3*a*b 3*b*\/ a*b
----- + ----- - ----- - -------- + --------- + ------- - -------------- + --------------- + ----- + -----------
a - b a - b a - b 2 a - b a - b 2 a - b a - b a - b
a - a*b a - a*b
$$- \frac{b^{\frac{5}{2}}}{a^{2} - a b} - \frac{2 b^{\frac{3}{2}} \sqrt{a b}}{a^{2} - a b} + \frac{a^{\frac{3}{2}}}{a - b} - \frac{b^{\frac{3}{2}}}{a - b} + \frac{\sqrt{a} b}{a - b} + \frac{2 \sqrt{a} \sqrt{a b}}{a - b} + \frac{3 a b}{a - b} + \frac{a \sqrt{a b}}{a - b} + \frac{b^{2}}{a - b} + \frac{3 b \sqrt{a b}}{a - b}$$
a^(3/2)/(a - b) + b^2/(a - b) - b^(3/2)/(a - b) - b^(5/2)/(a^2 - a*b) + a*sqrt(a*b)/(a - b) + b*sqrt(a)/(a - b) - 2*b^(3/2)*sqrt(a*b)/(a^2 - a*b) + 2*sqrt(a)*sqrt(a*b)/(a - b) + 3*a*b/(a - b) + 3*b*sqrt(a*b)/(a - b)
/ 3/2 3/2\
/ _____\ | _____ a - b |
\a + b + 2*\/ a*b /*|b + \/ a*b + -----------|
\ a /
-----------------------------------------------
a - b
$$\frac{\left(a + b + 2 \sqrt{a b}\right) \left(b + \sqrt{a b} + \frac{a^{\frac{3}{2}} - b^{\frac{3}{2}}}{a}\right)}{a - b}$$
/ 3/2 3/2\
/ ___ ___\ | ___ ___ a - b |
\a + b + 2*\/ a *\/ b /*|b + \/ a *\/ b + -----------|
\ a /
-------------------------------------------------------
a - b
$$\frac{\left(\sqrt{a} \sqrt{b} + b + \frac{a^{\frac{3}{2}} - b^{\frac{3}{2}}}{a}\right) \left(2 \sqrt{a} \sqrt{b} + a + b\right)}{a - b}$$
(a + b + 2*sqrt(a)*sqrt(b))*(b + sqrt(a)*sqrt(b) + (a^(3/2) - b^(3/2))/a)/(a - b)
5/2 5/2 3/2 3/2 3/2 _____ 3/2 _____ 2 _____
_____ a - b + b*a - a*b - 2*b *\/ a*b + 2*a *\/ a*b + 4*a*b + 4*a*b*\/ a*b
\/ a*b + 3*b + ----------------------------------------------------------------------------------------
2
a - a*b
$$3 b + \sqrt{a b} + \frac{a^{\frac{5}{2}} - b^{\frac{5}{2}} + a^{\frac{3}{2}} b + 2 a^{\frac{3}{2}} \sqrt{a b} - a b^{\frac{3}{2}} - 2 b^{\frac{3}{2}} \sqrt{a b} + 4 a b^{2} + 4 a b \sqrt{a b}}{a^{2} - a b}$$
sqrt(a*b) + 3*b + (a^(5/2) - b^(5/2) + b*a^(3/2) - a*b^(3/2) - 2*b^(3/2)*sqrt(a*b) + 2*a^(3/2)*sqrt(a*b) + 4*a*b^2 + 4*a*b*sqrt(a*b))/(a^2 - a*b)
Объединение рациональных выражений
[src]
/ _____\ / 3/2 3/2 _____\
\a + b + 2*\/ a*b /*\a - b + a*b + a*\/ a*b /
---------------------------------------------------
a*(a - b)
$$\frac{\left(a + b + 2 \sqrt{a b}\right) \left(a^{\frac{3}{2}} - b^{\frac{3}{2}} + a b + a \sqrt{a b}\right)}{a \left(a - b\right)}$$
(a + b + 2*sqrt(a*b))*(a^(3/2) - b^(3/2) + a*b + a*sqrt(a*b))/(a*(a - b))
/ _____\ / 3/2 3/2 _____\
\a + b + 2*\/ a*b /*\a - b + a*b + a*\/ a*b /
---------------------------------------------------
a*(a - b)
$$\frac{\left(a + b + 2 \sqrt{a b}\right) \left(a^{\frac{3}{2}} - b^{\frac{3}{2}} + a b + a \sqrt{a b}\right)}{a \left(a - b\right)}$$
(a + b + 2*sqrt(a*b))*(a^(3/2) - b^(3/2) + a*b + a*sqrt(a*b))/(a*(a - b))
/ ___ ___\
/ ___ ___\ | ___ ___ a*\/ a - b*\/ b |
\a + b + 2*\/ a *\/ b /*|b + \/ a *\/ b + -----------------|
\ a /
-------------------------------------------------------------
a - b
$$\frac{\left(\sqrt{a} \sqrt{b} + b + \frac{\sqrt{a} a - \sqrt{b} b}{a}\right) \left(2 \sqrt{a} \sqrt{b} + a + b\right)}{a - b}$$
(a + b + 2*sqrt(a)*sqrt(b))*(b + sqrt(a)*sqrt(b) + (a*sqrt(a) - b*sqrt(b))/a)/(a - b)
/ 3/2 3/2\
/ _____\ | _____ a - b |
\a + b + 2*\/ a*b /*|b + \/ a*b + -----------|
\ a /
-----------------------------------------------
a - b
$$\frac{\left(a + b + 2 \sqrt{a b}\right) \left(b + \sqrt{a b} + \frac{a^{\frac{3}{2}} - b^{\frac{3}{2}}}{a}\right)}{a - b}$$
(a + b + 2*sqrt(a*b))*(b + sqrt(a*b) + (a^(3/2) - b^(3/2))/a)/(a - b)