/ _____\ / ___ ___\ / 3/2 3/2\
(x - y)*\x + y - \/ x*y / + \\/ x + \/ y /*\x + y /
---------------------------------------------------------
/ ___ ___\ / _____\
\\/ x + \/ y /*\x + y - \/ x*y /
$$\frac{\left(\sqrt{x} + \sqrt{y}\right) \left(x^{\frac{3}{2}} + y^{\frac{3}{2}}\right) + \left(x - y\right) \left(x + y - \sqrt{x y}\right)}{\left(\sqrt{x} + \sqrt{y}\right) \left(x + y - \sqrt{x y}\right)}$$
((x - y)*(x + y - sqrt(x*y)) + (sqrt(x) + sqrt(y))*(x^(3/2) + y^(3/2)))/((sqrt(x) + sqrt(y))*(x + y - sqrt(x*y)))
Подстановка условия
[src]
(x*sqrt(x) + y*sqrt(y))/(x - sqrt(x*y) + y) + (x - y)/(sqrt(x) + sqrt(y)) при y = 1/3
___ ___
x*\/ x + y*\/ y x - y
----------------- + -------------
_____ ___ ___
x - \/ x*y + y \/ x + \/ y
$$\frac{\sqrt{x} x + \sqrt{y} y}{x + y - \sqrt{x y}} + \frac{x - y}{\sqrt{x} + \sqrt{y}}$$
/ _____\ / ___ ___\ / 3/2 3/2\
(x - y)*\x + y - \/ x*y / + \\/ x + \/ y /*\x + y /
---------------------------------------------------------
/ ___ ___\ / _____\
\\/ x + \/ y /*\x + y - \/ x*y /
$$\frac{\left(\sqrt{x} + \sqrt{y}\right) \left(x^{\frac{3}{2}} + y^{\frac{3}{2}}\right) + \left(x - y\right) \left(x + y - \sqrt{x y}\right)}{\left(\sqrt{x} + \sqrt{y}\right) \left(x + y - \sqrt{x y}\right)}$$
$$y = \frac{1}{3}$$
/ _________\ / ___ _______\ / 3/2 3/2\
(x - (1/3))*\x + (1/3) - \/ x*(1/3) / + \\/ x + \/ (1/3) /*\x + (1/3) /
-----------------------------------------------------------------------------
/ ___ _______\ / _________\
\\/ x + \/ (1/3) /*\x + (1/3) - \/ x*(1/3) /
$$\frac{\left(\sqrt{(1/3)} + \sqrt{x}\right) \left((1/3)^{\frac{3}{2}} + x^{\frac{3}{2}}\right) + \left(- (1/3) + x\right) \left((1/3) + x - \sqrt{(1/3) x}\right)}{\left(\sqrt{(1/3)} + \sqrt{x}\right) \left((1/3) + x - \sqrt{(1/3) x}\right)}$$
/ 1 _______\ / ___ 1 \ / 3/2 1 \
(x - 1/3)*|x + - - \/ x*1/3 | + |\/ x + -----|*|x + ----|
\ 3 / | ___| | 3/2|
\ \/ 3 / \ 3 /
-------------------------------------------------------------
/ ___ 1 \ / 1 _______\
|\/ x + -----|*|x + - - \/ x*1/3 |
| ___| \ 3 /
\ \/ 3 /
$$\frac{\left(\sqrt{x} + \sqrt{\frac{1}{3}}\right) \left(x^{\frac{3}{2}} + \left(\frac{1}{3}\right)^{\frac{3}{2}}\right) + \left(x - \frac{1}{3}\right) \left(x - \sqrt{x \frac{1}{3}} + \frac{1}{3}\right)}{\left(\sqrt{x} + \sqrt{\frac{1}{3}}\right) \left(x - \sqrt{x \frac{1}{3}} + \frac{1}{3}\right)}$$
/ ___ ___\ / ___\ / ___\
|1 \/ 3 *\/ x | | ___ \/ 3 | | 3/2 \/ 3 |
(-1/3 + x)*|- + x - -----------| + |\/ x + -----|*|x + -----|
\3 3 / \ 3 / \ 9 /
-----------------------------------------------------------------
/ ___\ / ___ ___\
| ___ \/ 3 | |1 \/ 3 *\/ x |
|\/ x + -----|*|- + x - -----------|
\ 3 / \3 3 /
$$\frac{\left(\sqrt{x} + \frac{\sqrt{3}}{3}\right) \left(x^{\frac{3}{2}} + \frac{\sqrt{3}}{9}\right) + \left(x - \frac{1}{3}\right) \left(- \frac{\sqrt{3} \sqrt{x}}{3} + x + \frac{1}{3}\right)}{\left(\sqrt{x} + \frac{\sqrt{3}}{3}\right) \left(- \frac{\sqrt{3} \sqrt{x}}{3} + x + \frac{1}{3}\right)}$$
((-1/3 + x)*(1/3 + x - sqrt(3)*sqrt(x)/3) + (sqrt(x) + sqrt(3)/3)*(x^(3/2) + sqrt(3)/9))/((sqrt(x) + sqrt(3)/3)*(1/3 + x - sqrt(3)*sqrt(x)/3))
Рациональный знаменатель
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3/2 3/2
x x y y
------------- + --------------- + --------------- - -------------
___ ___ _____ _____ ___ ___
\/ x + \/ y x + y - \/ x*y x + y - \/ x*y \/ x + \/ y
$$\frac{x^{\frac{3}{2}}}{x + y - \sqrt{x y}} + \frac{y^{\frac{3}{2}}}{x + y - \sqrt{x y}} + \frac{x}{\sqrt{x} + \sqrt{y}} - \frac{y}{\sqrt{x} + \sqrt{y}}$$
7/2 2 3/2 5/2 _____ ___ 3 3 ___ 3/2 2 5/2 _____ 3/2 _____ 3/2 _____
2*x + x *y + x *\/ x*y - \/ x *y - x *\/ y - x *y - y *\/ x*y + x*y *\/ x*y - y*x *\/ x*y
----------------------------------------------------------------------------------------------------------------
/ 2 2 \
(x - y)*\x + y + x*y/
$$\frac{2 x^{\frac{7}{2}} + x^{\frac{5}{2}} \sqrt{x y} - y^{\frac{5}{2}} \sqrt{x y} - x^{\frac{3}{2}} y^{2} - x^{\frac{3}{2}} y \sqrt{x y} + x^{2} y^{\frac{3}{2}} + x y^{\frac{3}{2}} \sqrt{x y} - \sqrt{x} y^{3} - x^{3} \sqrt{y}}{\left(x - y\right) \left(x^{2} + x y + y^{2}\right)}$$
(2*x^(7/2) + x^2*y^(3/2) + x^(5/2)*sqrt(x*y) - sqrt(x)*y^3 - x^3*sqrt(y) - x^(3/2)*y^2 - y^(5/2)*sqrt(x*y) + x*y^(3/2)*sqrt(x*y) - y*x^(3/2)*sqrt(x*y))/((x - y)*(x^2 + y^2 + x*y))
Объединение рациональных выражений
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/ _____\ / ___ ___\ / 3/2 3/2\
(x - y)*\x + y - \/ x*y / + \\/ x + \/ y /*\x + y /
---------------------------------------------------------
/ ___ ___\ / _____\
\\/ x + \/ y /*\x + y - \/ x*y /
$$\frac{\left(\sqrt{x} + \sqrt{y}\right) \left(x^{\frac{3}{2}} + y^{\frac{3}{2}}\right) + \left(x - y\right) \left(x + y - \sqrt{x y}\right)}{\left(\sqrt{x} + \sqrt{y}\right) \left(x + y - \sqrt{x y}\right)}$$
((x - y)*(x + y - sqrt(x*y)) + (sqrt(x) + sqrt(y))*(x^(3/2) + y^(3/2)))/((sqrt(x) + sqrt(y))*(x + y - sqrt(x*y)))
3/2 3/2
x - y x + y
------------- + ---------------
___ ___ _____
\/ x + \/ y x + y - \/ x*y
$$\frac{x^{\frac{3}{2}} + y^{\frac{3}{2}}}{x + y - \sqrt{x y}} + \frac{x - y}{\sqrt{x} + \sqrt{y}}$$
3/2 3/2
x - y x + y
------------- + ---------------
___ ___ _____
\/ x + \/ y x - \/ x*y + y
$$\frac{x^{\frac{3}{2}} + y^{\frac{3}{2}}}{x + y - \sqrt{x y}} + \frac{x - y}{\sqrt{x} + \sqrt{y}}$$
3/2 3/2
x - y x + y
------------- + -------------------
___ ___ ___ ___
\/ x + \/ y x + y - \/ x *\/ y
$$\frac{x^{\frac{3}{2}} + y^{\frac{3}{2}}}{- \sqrt{x} \sqrt{y} + x + y} + \frac{x - y}{\sqrt{x} + \sqrt{y}}$$
(x - y)/(sqrt(x) + sqrt(y)) + (x^(3/2) + y^(3/2))/(x + y - sqrt(x)*sqrt(y))
2 _____ ___ 3/2 3/2 ___ _____
2*x + y*\/ x*y + \/ x *y + x *\/ y - x*\/ x*y
------------------------------------------------------
/ ___ ___\ / _____\
\\/ x + \/ y /*\x + y - \/ x*y /
$$\frac{x^{\frac{3}{2}} \sqrt{y} + \sqrt{x} y^{\frac{3}{2}} + 2 x^{2} - x \sqrt{x y} + y \sqrt{x y}}{\left(\sqrt{x} + \sqrt{y}\right) \left(x + y - \sqrt{x y}\right)}$$
(2*x^2 + y*sqrt(x*y) + sqrt(x)*y^(3/2) + x^(3/2)*sqrt(y) - x*sqrt(x*y))/((sqrt(x) + sqrt(y))*(x + y - sqrt(x*y)))
2 _____ ___ 3/2 3/2 ___ _____
2*x + y*\/ x*y + \/ x *y + x *\/ y - x*\/ x*y
---------------------------------------------------------------
3/2 3/2 ___ ___ ___ _____ ___ _____
x + y + x*\/ y + y*\/ x - \/ x *\/ x*y - \/ y *\/ x*y
$$\frac{x^{\frac{3}{2}} \sqrt{y} + \sqrt{x} y^{\frac{3}{2}} + 2 x^{2} - x \sqrt{x y} + y \sqrt{x y}}{x^{\frac{3}{2}} + y^{\frac{3}{2}} + \sqrt{x} y - \sqrt{x} \sqrt{x y} + x \sqrt{y} - \sqrt{y} \sqrt{x y}}$$
(2*x^2 + y*sqrt(x*y) + sqrt(x)*y^(3/2) + x^(3/2)*sqrt(y) - x*sqrt(x*y))/(x^(3/2) + y^(3/2) + x*sqrt(y) + y*sqrt(x) - sqrt(x)*sqrt(x*y) - sqrt(y)*sqrt(x*y))
3/2 3/2
x - y x + y
------------- + ---------------
___ ___ _____
\/ x + \/ y x + y - \/ x*y
$$\frac{x^{\frac{3}{2}} + y^{\frac{3}{2}}}{x + y - \sqrt{x y}} + \frac{x - y}{\sqrt{x} + \sqrt{y}}$$
(x - y)/(sqrt(x) + sqrt(y)) + (x^(3/2) + y^(3/2))/(x + y - sqrt(x*y))
___ ___
x*\/ x + y*\/ y x - y
------------------- + -------------
___ ___ ___ ___
x + y - \/ x *\/ y \/ x + \/ y
$$\frac{\sqrt{x} x + \sqrt{y} y}{- \sqrt{x} \sqrt{y} + x + y} + \frac{x - y}{\sqrt{x} + \sqrt{y}}$$
(x*sqrt(x) + y*sqrt(y))/(x + y - sqrt(x)*sqrt(y)) + (x - y)/(sqrt(x) + sqrt(y))