/ ___\ // ___\ / ___\ / ___\\
(-1 + a)*\1 + a + 2*\/ 2 / - a*\\-2 + \/ a /*\1 + a + 2*\/ 2 / - (-1 + a)*\2 + \/ a //
--------------------------------------------------------------------------------------
___ / ___\
\/ a *(-1 + a)*\1 + a + 2*\/ 2 /
$$\frac{- a \left(\left(\sqrt{a} - 2\right) \left(a + 1 + 2 \sqrt{2}\right) - \left(\sqrt{a} + 2\right) \left(a - 1\right)\right) + \left(a - 1\right) \left(a + 1 + 2 \sqrt{2}\right)}{\sqrt{a} \left(a - 1\right) \left(a + 1 + 2 \sqrt{2}\right)}$$
((-1 + a)*(1 + a + 2*sqrt(2)) - a*((-2 + sqrt(a))*(1 + a + 2*sqrt(2)) - (-1 + a)*(2 + sqrt(a))))/(sqrt(a)*(-1 + a)*(1 + a + 2*sqrt(2)))
a^(-0.5) + a^0.5*((2.0 + a^0.5)/(3.82842712474619 + a) - (-2.0 + a^0.5)/(-1.0 + a))
a^(-0.5) + a^0.5*((2.0 + a^0.5)/(3.82842712474619 + a) - (-2.0 + a^0.5)/(-1.0 + a))
/ ___ ___\
1 ___ | 2 + \/ a -2 + \/ a |
----- + \/ a *|--------------- - ----------|
___ | ___ -1 + a |
\/ a \1 + a + 2*\/ 2 /
$$\sqrt{a} \left(- \frac{\sqrt{a} - 2}{a - 1} + \frac{\sqrt{a} + 2}{a + 1 + 2 \sqrt{2}}\right) + \frac{1}{\sqrt{a}}$$
/ ___ ___ \
1 ___ |2 - \/ a 2 + \/ a |
----- + \/ a *|--------- + ---------------|
___ | -1 + a ___|
\/ a \ 1 + a + 2*\/ 2 /
$$\sqrt{a} \left(\frac{- \sqrt{a} + 2}{a - 1} + \frac{\sqrt{a} + 2}{a + 1 + 2 \sqrt{2}}\right) + \frac{1}{\sqrt{a}}$$
/ ___ ___ \
1 ___ |2 - \/ a 2 + \/ a |
----- + \/ a *|--------- + ---------------|
___ | a - 1 ___ |
\/ a \ a + 2*\/ 2 + 1/
$$\sqrt{a} \left(\frac{- \sqrt{a} + 2}{a - 1} + \frac{\sqrt{a} + 2}{a + 1 + 2 \sqrt{2}}\right) + \frac{1}{\sqrt{a}}$$
1/sqrt(a) + sqrt(a)*((2 - sqrt(a))/(a - 1*1) + (2 + sqrt(a))/(a + 2*sqrt(2) + 1))
5/2 ___ ___ 3/2 2 ___ ___ ___
-1 + a - \/ a - 2*\/ 2 - 2*a + 5*a - 2*\/ 2 *\/ a + 6*a*\/ 2
-1 + -----------------------------------------------------------------------
5/2 ___ ___ ___ ___ 3/2
a - \/ a - 2*\/ 2 *\/ a + 2*\/ 2 *a
$$-1 + \frac{a^{\frac{5}{2}} - 2 a^{\frac{3}{2}} + 5 a^{2} - 2 \sqrt{2} \sqrt{a} - \sqrt{a} + 6 \sqrt{2} a - 2 \sqrt{2} - 1}{a^{\frac{5}{2}} + 2 \sqrt{2} a^{\frac{3}{2}} - 2 \sqrt{2} \sqrt{a} - \sqrt{a}}$$
-1 + (-1 + a^(5/2) - sqrt(a) - 2*sqrt(2) - 2*a^(3/2) + 5*a^2 - 2*sqrt(2)*sqrt(a) + 6*a*sqrt(2))/(a^(5/2) - sqrt(a) - 2*sqrt(2)*sqrt(a) + 2*sqrt(2)*a^(3/2))
Рациональный знаменатель
[src]
___ ___
1 a a 2*\/ a 2*\/ a
----- + --------------- - ------ + ------- + ---------------
___ ___ -1 + a -1 + a ___
\/ a 1 + a + 2*\/ 2 1 + a + 2*\/ 2
$$\frac{2 \sqrt{a}}{a + 1 + 2 \sqrt{2}} + \frac{2 \sqrt{a}}{a - 1} + \frac{a}{a + 1 + 2 \sqrt{2}} - \frac{a}{a - 1} + \frac{1}{\sqrt{a}}$$
5/2 2 3 3/2 ___ 2 ___ 5/2 ___ 3/2 ___
7 - 25*a - 2*a + 5*a + 5*a + 6*a - 4*\/ 2 *a - 2*\/ 2 *a + 2*\/ 2 *a + 4*a*\/ 2
-----------------------------------------------------------------------------------------------
___ / 2 \
\/ a *(-1 + a)*\-7 + a + 2*a/
$$\frac{- 2 \sqrt{2} a^{\frac{5}{2}} - 2 a^{\frac{5}{2}} + 2 \sqrt{2} a^{\frac{3}{2}} + 6 a^{\frac{3}{2}} + 5 a^{3} - 4 \sqrt{2} a^{2} + 5 a^{2} - 25 a + 4 \sqrt{2} a + 7}{\sqrt{a} \left(a - 1\right) \left(a^{2} + 2 a - 7\right)}$$
(7 - 25*a - 2*a^(5/2) + 5*a^2 + 5*a^3 + 6*a^(3/2) - 4*sqrt(2)*a^2 - 2*sqrt(2)*a^(5/2) + 2*sqrt(2)*a^(3/2) + 4*a*sqrt(2))/(sqrt(a)*(-1 + a)*(-7 + a^2 + 2*a))
/ ___ ___\
1 ___ | 2 + \/ a -2 + \/ a |
----- + \/ a *|--------------- - ----------|
___ | ___ -1 + a |
\/ a \1 + a + 2*\/ 2 /
$$\sqrt{a} \left(- \frac{\sqrt{a} - 2}{a - 1} + \frac{\sqrt{a} + 2}{a + 1 + 2 \sqrt{2}}\right) + \frac{1}{\sqrt{a}}$$
1/sqrt(a) + sqrt(a)*((2 + sqrt(a))/(1 + a + 2*sqrt(2)) - (-2 + sqrt(a))/(-1 + a))
___ 3/2 2 ___ 3/2 ___
-1 - 2*\/ 2 - 2*a + 5*a - 2*\/ 2 *a + 6*a*\/ 2
-------------------------------------------------------
___ / ___\
\/ a *(-1 + a)*\1 + a + 2*\/ 2 /
$$\frac{- 2 \sqrt{2} a^{\frac{3}{2}} - 2 a^{\frac{3}{2}} + 5 a^{2} + 6 \sqrt{2} a - 2 \sqrt{2} - 1}{\sqrt{a} \left(a - 1\right) \left(a + 1 + 2 \sqrt{2}\right)}$$
(-1 - 2*sqrt(2) - 2*a^(3/2) + 5*a^2 - 2*sqrt(2)*a^(3/2) + 6*a*sqrt(2))/(sqrt(a)*(-1 + a)*(1 + a + 2*sqrt(2)))
Объединение рациональных выражений
[src]
/ / ___\ / ___\ / ___\\ / ___\
a*\(-1 + a)*\2 + \/ a / - \-2 + \/ a /*\1 + a + 2*\/ 2 // + (-1 + a)*\1 + a + 2*\/ 2 /
--------------------------------------------------------------------------------------
___ / ___\
\/ a *(-1 + a)*\1 + a + 2*\/ 2 /
$$\frac{a \left(- \left(\sqrt{a} - 2\right) \left(a + 1 + 2 \sqrt{2}\right) + \left(\sqrt{a} + 2\right) \left(a - 1\right)\right) + \left(a - 1\right) \left(a + 1 + 2 \sqrt{2}\right)}{\sqrt{a} \left(a - 1\right) \left(a + 1 + 2 \sqrt{2}\right)}$$
(a*((-1 + a)*(2 + sqrt(a)) - (-2 + sqrt(a))*(1 + a + 2*sqrt(2))) + (-1 + a)*(1 + a + 2*sqrt(2)))/(sqrt(a)*(-1 + a)*(1 + a + 2*sqrt(2)))