Господин Экзамен
Упрощение выражений/
Общий знаменатель/
((x-y)/(x^(3/4)+x^(1/2)*y^(1/4))-(x^(1/2)-y^(1/2))/(x^(1/4)+y^(1/4)))*(y/x)^(-(1/2))
Общий знаменатель ((x-y)/(x^(3/4)+x^(1/2)*y^(1/4))-(x^(1/2)-y^(1/2))/(x^(1/4)+y^(1/4)))*(y/x)^(-(1/2))
Решение
Вы ввели
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___ ___
x - y \/ x - \/ y
------------------ - -------------
3/4 ___ 4 ___ 4 ___ 4 ___
x + \/ x *\/ y \/ x + \/ y
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___
/ y
/ -
\/ x
$$\frac{\frac{x - y}{x^{\frac{3}{4}} + \sqrt{x} \sqrt[4]{y}} - \frac{\sqrt{x} - \sqrt{y}}{\sqrt[4]{x} + \sqrt[4]{y}}}{\sqrt{\frac{y}{x}}}$$
((x - y)/(x^(3/4) + sqrt(x)*y^(1/4)) - (sqrt(x) - sqrt(y))/(x^(1/4) + y^(1/4)))/sqrt(y/x)
Общее упрощение
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5/4 ___ 3/4 3/4 ___ 4 ___
- y + \/ x *y + x *\/ y - y*\/ x
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___
/ y / ___ ___ 3/4 4 ___\
/ - *\x + \/ x *\/ y + 2*x *\/ y /
\/ x
$$\frac{- y^{\frac{5}{4}} + x^{\frac{3}{4}} \sqrt{y} + \sqrt{x} y^{\frac{3}{4}} - \sqrt[4]{x} y}{\sqrt{\frac{y}{x}} \left(2 x^{\frac{3}{4}} \sqrt[4]{y} + \sqrt{x} \sqrt{y} + x\right)}$$
(-y^(5/4) + sqrt(x)*y^(3/4) + x^(3/4)*sqrt(y) - y*x^(1/4))/(sqrt(y/x)*(x + sqrt(x)*sqrt(y) + 2*x^(3/4)*y^(1/4)))
Численный ответ
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((x - y)/(x^0.75 + x^0.5*y^0.25) - (x^0.5 - y^0.5)/(x^0.25 + y^0.25))/(y/x)^0.5
((x - y)/(x^0.75 + x^0.5*y^0.25) - (x^0.5 - y^0.5)/(x^0.25 + y^0.25))/(y/x)^0.5
Общий знаменатель
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5/4 ___ 3/4 3/4 ___ 4 ___
- y + \/ x *y + x *\/ y - y*\/ x
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___ ___ ___
/ y ___ ___ / y 3/4 4 ___ / y
x* / - + \/ x *\/ y * / - + 2*x *\/ y * / -
\/ x \/ x \/ x
$$\frac{- y^{\frac{5}{4}} + x^{\frac{3}{4}} \sqrt{y} + \sqrt{x} y^{\frac{3}{4}} - \sqrt[4]{x} y}{2 x^{\frac{3}{4}} \sqrt[4]{y} \sqrt{\frac{y}{x}} + \sqrt{x} \sqrt{y} \sqrt{\frac{y}{x}} + x \sqrt{\frac{y}{x}}}$$
(-y^(5/4) + sqrt(x)*y^(3/4) + x^(3/4)*sqrt(y) - y*x^(1/4))/(x*sqrt(y/x) + sqrt(x)*sqrt(y)*sqrt(y/x) + 2*x^(3/4)*y^(1/4)*sqrt(y/x))
Объединение рациональных выражений
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/4 ___ 4 ___\ / ___ ___\ / 3/4 ___ 4 ___\
(x - y)*\\/ x + \/ y / - \\/ x - \/ y /*\x + \/ x *\/ y /
--------------------------------------------------------------
___
/ y /4 ___ 4 ___\ / 3/4 ___ 4 ___\
/ - *\\/ x + \/ y /*\x + \/ x *\/ y /
\/ x
$$\frac{\left(\sqrt[4]{x} + \sqrt[4]{y}\right) \left(x - y\right) - \left(\sqrt{x} - \sqrt{y}\right) \left(x^{\frac{3}{4}} + \sqrt{x} \sqrt[4]{y}\right)}{\sqrt{\frac{y}{x}} \left(\sqrt[4]{x} + \sqrt[4]{y}\right) \left(x^{\frac{3}{4}} + \sqrt{x} \sqrt[4]{y}\right)}$$
((x - y)*(x^(1/4) + y^(1/4)) - (sqrt(x) - sqrt(y))*(x^(3/4) + sqrt(x)*y^(1/4)))/(sqrt(y/x)*(x^(1/4) + y^(1/4))*(x^(3/4) + sqrt(x)*y^(1/4)))
Рациональный знаменатель
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___ ___
x \/ y y \/ x
---------------------------------- + ----------------------------- - ---------------------------------- - -----------------------------
___ ___ ___ ___ ___ ___ ___ ___
3/4 / y ___ 4 ___ / y 4 ___ / y 4 ___ / y 3/4 / y ___ 4 ___ / y 4 ___ / y 4 ___ / y
x * / - + \/ x *\/ y * / - \/ x * / - + \/ y * / - x * / - + \/ x *\/ y * / - \/ x * / - + \/ y * / -
\/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x
$$- \frac{\sqrt{x}}{\sqrt[4]{x} \sqrt{\frac{y}{x}} + \sqrt[4]{y} \sqrt{\frac{y}{x}}} + \frac{x}{x^{\frac{3}{4}} \sqrt{\frac{y}{x}} + \sqrt{x} \sqrt[4]{y} \sqrt{\frac{y}{x}}} + \frac{\sqrt{y}}{\sqrt[4]{x} \sqrt{\frac{y}{x}} + \sqrt[4]{y} \sqrt{\frac{y}{x}}} - \frac{y}{x^{\frac{3}{4}} \sqrt{\frac{y}{x}} + \sqrt{x} \sqrt[4]{y} \sqrt{\frac{y}{x}}}$$
______ ___ ______ ___ _________ ___ _________ ___ _________ ___ _________ ___ ______ ___ ______ ___ ____ ______ ___ ____ _________ ___ ____ _________ ___ ____ ______ ___ ____ _________ ___ ____ ______ ___ ____ ______ ___ ____ _________ ___
7/2 / 3/2 / y 2 5/2 / 3/2 / y 3 3/2 / ___ / y 5/2 2 / ___ / y 7/2 / ___ / y 2 5/2 / ___ / y 3 3/2 / 3/2 / y 5/2 2 / 3/2 / y 2 / 3 / 3/2 / y 2 / 3 / ___ / y 3/2 3/2 / 3 / ___ / y 5/2 ___ / 3 / 3/2 / y 2 / 3 / ___ / y 2 / 3 / 3/2 / y 3/2 3/2 / 3 / 3/2 / y 5/2 ___ / 3 / ___ / y
y*x *\/ x * / - + x *y *\/ x * / - + x *y *\/ x*\/ y * / - + x *y *\/ x*\/ y * / - - y*x *\/ x*\/ y * / - - x *y *\/ x*\/ y * / - - x *y *\/ x * / - - x *y *\/ x * / - + x*y *\/ x *\/ x * / - + y*x *\/ x *\/ x*\/ y * / - + x *y *\/ x *\/ x*\/ y * / - + x *\/ y *\/ x *\/ x * / - - x*y *\/ x *\/ x*\/ y * / - - y*x *\/ x *\/ x * / - - x *y *\/ x *\/ x * / - - x *\/ y *\/ x *\/ x*\/ y * / -
\/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x \/ x
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/ 3 2\
y*(x - y)*\x - y*x /
$$\frac{- x^{\frac{7}{2}} y \sqrt{\frac{y}{x}} \sqrt{x \sqrt{y}} + x^{\frac{7}{2}} y \sqrt{\frac{y}{x}} \sqrt{x^{\frac{3}{2}}} - x^{\frac{5}{2}} \sqrt{y} \sqrt{\frac{y}{x}} \sqrt{x \sqrt{y}} \sqrt{x^{3}} + x^{\frac{5}{2}} \sqrt{y} \sqrt{\frac{y}{x}} \sqrt{x^{\frac{3}{2}}} \sqrt{x^{3}} + x^{\frac{5}{2}} y^{2} \sqrt{\frac{y}{x}} \sqrt{x \sqrt{y}} - x^{\frac{5}{2}} y^{2} \sqrt{\frac{y}{x}} \sqrt{x^{\frac{3}{2}}} + x^{\frac{3}{2}} y^{\frac{3}{2}} \sqrt{\frac{y}{x}} \sqrt{x \sqrt{y}} \sqrt{x^{3}} - x^{\frac{3}{2}} y^{\frac{3}{2}} \sqrt{\frac{y}{x}} \sqrt{x^{\frac{3}{2}}} \sqrt{x^{3}} - x^{2} y^{\frac{5}{2}} \sqrt{\frac{y}{x}} \sqrt{x \sqrt{y}} + x^{2} y^{\frac{5}{2}} \sqrt{\frac{y}{x}} \sqrt{x^{\frac{3}{2}}} + x^{3} y^{\frac{3}{2}} \sqrt{\frac{y}{x}} \sqrt{x \sqrt{y}} - x^{3} y^{\frac{3}{2}} \sqrt{\frac{y}{x}} \sqrt{x^{\frac{3}{2}}} + x^{2} y \sqrt{\frac{y}{x}} \sqrt{x \sqrt{y}} \sqrt{x^{3}} - x^{2} y \sqrt{\frac{y}{x}} \sqrt{x^{\frac{3}{2}}} \sqrt{x^{3}} - x y^{2} \sqrt{\frac{y}{x}} \sqrt{x \sqrt{y}} \sqrt{x^{3}} + x y^{2} \sqrt{\frac{y}{x}} \sqrt{x^{\frac{3}{2}}} \sqrt{x^{3}}}{y \left(x - y\right) \left(x^{3} - x^{2} y\right)}$$
(y*x^(7/2)*sqrt(x^(3/2))*sqrt(y/x) + x^2*y^(5/2)*sqrt(x^(3/2))*sqrt(y/x) + x^3*y^(3/2)*sqrt(x*sqrt(y))*sqrt(y/x) + x^(5/2)*y^2*sqrt(x*sqrt(y))*sqrt(y/x) - y*x^(7/2)*sqrt(x*sqrt(y))*sqrt(y/x) - x^2*y^(5/2)*sqrt(x*sqrt(y))*sqrt(y/x) - x^3*y^(3/2)*sqrt(x^(3/2))*sqrt(y/x) - x^(5/2)*y^2*sqrt(x^(3/2))*sqrt(y/x) + x*y^2*sqrt(x^3)*sqrt(x^(3/2))*sqrt(y/x) + y*x^2*sqrt(x^3)*sqrt(x*sqrt(y))*sqrt(y/x) + x^(3/2)*y^(3/2)*sqrt(x^3)*sqrt(x*sqrt(y))*sqrt(y/x) + x^(5/2)*sqrt(y)*sqrt(x^3)*sqrt(x^(3/2))*sqrt(y/x) - x*y^2*sqrt(x^3)*sqrt(x*sqrt(y))*sqrt(y/x) - y*x^2*sqrt(x^3)*sqrt(x^(3/2))*sqrt(y/x) - x^(3/2)*y^(3/2)*sqrt(x^3)*sqrt(x^(3/2))*sqrt(y/x) - x^(5/2)*sqrt(y)*sqrt(x^3)*sqrt(x*sqrt(y))*sqrt(y/x))/(y*(x - y)*(x^3 - y*x^2))
Степени
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___ ___
\/ y - \/ x x - y
------------- + ------------------
4 ___ 4 ___ 3/4 ___ 4 ___
\/ x + \/ y x + \/ x *\/ y
----------------------------------
___
/ y
/ -
\/ x
$$\frac{\frac{x - y}{x^{\frac{3}{4}} + \sqrt{x} \sqrt[4]{y}} + \frac{- \sqrt{x} + \sqrt{y}}{\sqrt[4]{x} + \sqrt[4]{y}}}{\sqrt{\frac{y}{x}}}$$
/ ___ ___ \
___ |\/ y - \/ x x - y |
\/ x *|------------- + ------------------|
|4 ___ 4 ___ 3/4 ___ 4 ___|
\\/ x + \/ y x + \/ x *\/ y /
------------------------------------------
___
\/ y
$$\frac{\sqrt{x} \left(\frac{x - y}{x^{\frac{3}{4}} + \sqrt{x} \sqrt[4]{y}} + \frac{- \sqrt{x} + \sqrt{y}}{\sqrt[4]{x} + \sqrt[4]{y}}\right)}{\sqrt{y}}$$
sqrt(x)*((sqrt(y) - sqrt(x))/(x^(1/4) + y^(1/4)) + (x - y)/(x^(3/4) + sqrt(x)*y^(1/4)))/sqrt(y)
Комбинаторика
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/ 5/4 4 ___ ___ 3/4 3/4 ___\
-\y + y*\/ x - \/ x *y - x *\/ y /
--------------------------------------------
___
/ y /4 ___ 4 ___\ / 3/4 ___ 4 ___\
/ - *\\/ x + \/ y /*\x + \/ x *\/ y /
\/ x
$$- \frac{y^{\frac{5}{4}} - x^{\frac{3}{4}} \sqrt{y} - \sqrt{x} y^{\frac{3}{4}} + \sqrt[4]{x} y}{\sqrt{\frac{y}{x}} \left(\sqrt[4]{x} + \sqrt[4]{y}\right) \left(x^{\frac{3}{4}} + \sqrt{x} \sqrt[4]{y}\right)}$$
-(y^(5/4) + y*x^(1/4) - sqrt(x)*y^(3/4) - x^(3/4)*sqrt(y))/(sqrt(y/x)*(x^(1/4) + y^(1/4))*(x^(3/4) + sqrt(x)*y^(1/4)))