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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(sqrt(2)/a+a/sqrt(2)+2)-(a^2*sqrt(sqrt(2))-2*sqrt(a))/(a*sqrt(2*a)-sqrt(sqrt(8*a^4)))

¿Cómo vas a descomponer esta sqrt(sqrt(2)/a+a/sqrt(2)+2)-(a^2*sqrt(sqrt(2))-2*sqrt(a))/(a*sqrt(2*a)-sqrt(sqrt(8*a^4))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
      ___________________           _______            
     /   ___                   2   /   ___        ___  
    /  \/ 2      a            a *\/  \/ 2   - 2*\/ a   
   /   ----- + ----- + 2  - ---------------------------
  /      a       ___                        ___________
\/             \/ 2                        /    ______ 
                                _____     /    /    4  
                            a*\/ 2*a  - \/   \/  8*a
−−2a+a22a2a−8a4+(a2+2a)+2- \frac{- 2 \sqrt{a} + a^{2} \sqrt{\sqrt{2}}}{a \sqrt{2 a} - \sqrt{\sqrt{8 a^{4}}}} + \sqrt{\left(\frac{a}{\sqrt{2}} + \frac{\sqrt{2}}{a}\right) + 2} 
sqrt(sqrt(2)/a + a/sqrt(2) + 2) - (a^2*sqrt(sqrt(2)) - 2*sqrt(a))/(a*sqrt(2*a) - sqrt(sqrt(8*a^4)))
Simplificación general [src] 
                                __________________________                            
                               /     ___           ___  2  /                     ____\
                       ___    /  2*\/ 2  + 4*a + \/ 2 *a   |  ___  3/2    3/4 4 /  4 |
                     \/ 2 *  /   ------------------------ *\\/ 2 *a    - 2   *\/  a  /
    ___   4 ___  2         \/               a                                         
2*\/ a  - \/ 2 *a  + -----------------------------------------------------------------
                                                     2                                
--------------------------------------------------------------------------------------
                                                   ____                               
                                ___  3/2    3/4 4 /  4                                
                              \/ 2 *a    - 2   *\/  a
2a−24a2+22a2+4a+22a(2a32−234a44)22a32−234a44\frac{2 \sqrt{a} - \sqrt[4]{2} a^{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{2} a^{2} + 4 a + 2 \sqrt{2}}{a}} \left(\sqrt{2} a^{\frac{3}{2}} - 2^{\frac{3}{4}} \sqrt[4]{a^{4}}\right)}{2}}{\sqrt{2} a^{\frac{3}{2}} - 2^{\frac{3}{4}} \sqrt[4]{a^{4}}} 
(2*sqrt(a) - 2^(1/4)*a^2 + sqrt(2)*sqrt((2*sqrt(2) + 4*a + sqrt(2)*a^2)/a)*(sqrt(2)*a^(3/2) - 2^(3/4)*(a^4)^(1/4))/2)/(sqrt(2)*a^(3/2) - 2^(3/4)*(a^4)^(1/4))
Respuesta numérica [src] 
1.4142135623731*(1 + 0.353553390593274*a + 0.707106781186548/a)^0.5 - (1.18920711500272*a^2 - 2.0*a^0.5)/(1.4142135623731*a^1.5 - 1.68179283050743*(a^4)^0.25)
1.4142135623731*(1 + 0.353553390593274*a + 0.707106781186548/a)^0.5 - (1.18920711500272*a^2 - 2.0*a^0.5)/(1.4142135623731*a^1.5 - 1.68179283050743*(a^4)^0.25)
Compilar la expresión [src] 
     _____________________                            
    /       ___       ___             ___   4 ___  2  
   /      \/ 2    a*\/ 2        - 2*\/ a  + \/ 2 *a   
  /   2 + ----- + -------  - -------------------------
\/          a        2                            ____
                               ___  3/2    3/4 4 /  4 
                             \/ 2 *a    - 2   *\/  a
−−2a+24a22a32−234a44+2a2+2+2a- \frac{- 2 \sqrt{a} + \sqrt[4]{2} a^{2}}{\sqrt{2} a^{\frac{3}{2}} - 2^{\frac{3}{4}} \sqrt[4]{a^{4}}} + \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} 
sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) - (-2*sqrt(a) + 2^(1/4)*a^2)/(sqrt(2)*a^(3/2) - 2^(3/4)*(a^4)^(1/4))
Denominador común [src] 
     _____________________                            
    /       ___       ___             ___   4 ___  2  
   /      \/ 2    a*\/ 2        - 2*\/ a  + \/ 2 *a   
  /   2 + ----- + -------  + -------------------------
\/          a        2               ____             
                              3/4 4 /  4      ___  3/2
                             2   *\/  a   - \/ 2 *a
−2a+24a2−2a32+234a44+2a2+2+2a\frac{- 2 \sqrt{a} + \sqrt[4]{2} a^{2}}{- \sqrt{2} a^{\frac{3}{2}} + 2^{\frac{3}{4}} \sqrt[4]{a^{4}}} + \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} 
sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) + (-2*sqrt(a) + 2^(1/4)*a^2)/(2^(3/4)*(a^4)^(1/4) - sqrt(2)*a^(3/2))
Potencias [src] 
     _____________________                            
    /       ___       ___             ___   4 ___  2  
   /      \/ 2    a*\/ 2        - 2*\/ a  + \/ 2 *a   
  /   2 + ----- + -------  - -------------------------
\/          a        2                            ____
                               ___  3/2    3/4 4 /  4 
                             \/ 2 *a    - 2   *\/  a
−−2a+24a22a32−234a44+2a2+2+2a- \frac{- 2 \sqrt{a} + \sqrt[4]{2} a^{2}}{\sqrt{2} a^{\frac{3}{2}} - 2^{\frac{3}{4}} \sqrt[4]{a^{4}}} + \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} 
     _____________________                            
    /       ___       ___            ___   4 ___  2   
   /      \/ 2    a*\/ 2         2*\/ a  - \/ 2 *a    
  /   2 + ----- + -------  + -------------------------
\/          a        2                            ____
                               ___  3/2    3/4 4 /  4 
                             \/ 2 *a    - 2   *\/  a
2a−24a22a32−234a44+2a2+2+2a\frac{2 \sqrt{a} - \sqrt[4]{2} a^{2}}{\sqrt{2} a^{\frac{3}{2}} - 2^{\frac{3}{4}} \sqrt[4]{a^{4}}} + \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} 
sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) + (2*sqrt(a) - 2^(1/4)*a^2)/(sqrt(2)*a^(3/2) - 2^(3/4)*(a^4)^(1/4))
Abrimos la expresión [src] 
      ___________________          _______           
     /   ___                  2   /   ___        ___ 
    /  \/ 2      a           a *\/  \/ 2   - 2*\/ a  
   /   ----- + ----- + 2  - -------------------------
  /      a       ___                             ____
\/             \/ 2           ___  3/2    3/4 4 /  4 
                            \/ 2 *a    - 2   *\/  a
−−2a+a222a32−234a44+(a2+2a)+2- \frac{- 2 \sqrt{a} + a^{2} \sqrt{\sqrt{2}}}{\sqrt{2} a^{\frac{3}{2}} - 2^{\frac{3}{4}} \sqrt[4]{a^{4}}} + \sqrt{\left(\frac{a}{\sqrt{2}} + \frac{\sqrt{2}}{a}\right) + 2} 
sqrt(sqrt(2)/a + a/sqrt(2) + 2) - (a^2*sqrt(sqrt(2)) - 2*sqrt(a))/(sqrt(2)*a^(3/2) - 2^(3/4)*(a^4)^(1/4))
Unión de expresiones racionales [src] 
                                  ______________________                            
                                 /         ___ /     2\  /                     ____\
    ___     4 ___  2     ___    /  4*a + \/ 2 *\2 + a /  |  ___  3/2    3/4 4 /  4 |
4*\/ a  - 2*\/ 2 *a  + \/ 2 *  /   -------------------- *\\/ 2 *a    - 2   *\/  a  /
                             \/             a                                       
------------------------------------------------------------------------------------
                             /                     ____\                            
                             |  ___  3/2    3/4 4 /  4 |                            
                           2*\\/ 2 *a    - 2   *\/  a  /
4a−224a2+24a+2(a2+2)a(2a32−234a44)2(2a32−234a44)\frac{4 \sqrt{a} - 2 \sqrt[4]{2} a^{2} + \sqrt{2} \sqrt{\frac{4 a + \sqrt{2} \left(a^{2} + 2\right)}{a}} \left(\sqrt{2} a^{\frac{3}{2}} - 2^{\frac{3}{4}} \sqrt[4]{a^{4}}\right)}{2 \left(\sqrt{2} a^{\frac{3}{2}} - 2^{\frac{3}{4}} \sqrt[4]{a^{4}}\right)} 
(4*sqrt(a) - 2*2^(1/4)*a^2 + sqrt(2)*sqrt((4*a + sqrt(2)*(2 + a^2))/a)*(sqrt(2)*a^(3/2) - 2^(3/4)*(a^4)^(1/4)))/(2*(sqrt(2)*a^(3/2) - 2^(3/4)*(a^4)^(1/4)))
Parte trigonométrica [src] 
     _____________________                            
    /       ___       ___             ___   4 ___  2  
   /      \/ 2    a*\/ 2        - 2*\/ a  + \/ 2 *a   
  /   2 + ----- + -------  - -------------------------
\/          a        2                            ____
                               ___  3/2    3/4 4 /  4 
                             \/ 2 *a    - 2   *\/  a
−−2a+24a22a32−234a44+2a2+2+2a- \frac{- 2 \sqrt{a} + \sqrt[4]{2} a^{2}}{\sqrt{2} a^{\frac{3}{2}} - 2^{\frac{3}{4}} \sqrt[4]{a^{4}}} + \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} 
sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) - (-2*sqrt(a) + 2^(1/4)*a^2)/(sqrt(2)*a^(3/2) - 2^(3/4)*(a^4)^(1/4))
Combinatoria [src] 
                                 _______________________                      _______________________
                                /                   ___             ____     /                   ___ 
      ___   4 ___  2    3/2    /          ___   2*\/ 2     4 ___ 4 /  4     /          ___   2*\/ 2  
- 2*\/ a  + \/ 2 *a  - a   *  /   4 + a*\/ 2  + -------  + \/ 2 *\/  a  *  /   4 + a*\/ 2  + ------- 
                            \/                     a                     \/                     a    
-----------------------------------------------------------------------------------------------------
                                              ____                                                   
                                       3/4 4 /  4      ___  3/2                                      
                                      2   *\/  a   - \/ 2 *a
−a322a+4+22a−2a+24a2+242a+4+22aa44−2a32+234a44\frac{- a^{\frac{3}{2}} \sqrt{\sqrt{2} a + 4 + \frac{2 \sqrt{2}}{a}} - 2 \sqrt{a} + \sqrt[4]{2} a^{2} + \sqrt[4]{2} \sqrt{\sqrt{2} a + 4 + \frac{2 \sqrt{2}}{a}} \sqrt[4]{a^{4}}}{- \sqrt{2} a^{\frac{3}{2}} + 2^{\frac{3}{4}} \sqrt[4]{a^{4}}} 
(-2*sqrt(a) + 2^(1/4)*a^2 - a^(3/2)*sqrt(4 + a*sqrt(2) + 2*sqrt(2)/a) + 2^(1/4)*(a^4)^(1/4)*sqrt(4 + a*sqrt(2) + 2*sqrt(2)/a))/(2^(3/4)*(a^4)^(1/4) - sqrt(2)*a^(3/2))
Denominador racional [src] 
                                                                      _____________________                                                                                                              _____________________                                                  _____________________                             _____________________                             _____________________                            _____________________                                   _____________________                                  _____________________
          ____             ____              ____           ____     /       ___       ___                  ____                 ____                   ____                  ____             ____     /       ___       ___                    ____                 ____     /       ___       ___                    ____     /       ___       ___                    ____     /       ___       ___                   ____     /       ___       ___                  ____    ____     /       ___       ___                 ____    ____     /       ___       ___ 
     5 4 /  4       5/2   /  3     3/4  5   /  3       2   /  4     /      \/ 2    a*\/ 2         ___  4 4 /  4      4 ___  4   /  3        ___  7/2   /  3       3/4  7/2 4 /  4       9/2   /  3     /      \/ 2    a*\/ 2       4 ___  5/2 4 /  4        ___  3   /  4     /      \/ 2    a*\/ 2         ___  7/2   /  3     /      \/ 2    a*\/ 2       4 ___  9/2 4 /  4     /      \/ 2    a*\/ 2        3/4  7/2 4 /  4     /      \/ 2    a*\/ 2       4 ___  3   /  3  4 /  4     /      \/ 2    a*\/ 2        3/4  2   /  3  4 /  4     /      \/ 2    a*\/ 2  
- 2*a *\/  a   + 4*a   *\/  a   - 2   *a *\/  a   - 4*a *\/  a  *  /   2 + ----- + -------  - 2*\/ 2 *a *\/  a   - 2*\/ 2 *a *\/  a   + 2*\/ 2 *a   *\/  a   + 2*2   *a   *\/  a   + 2*a   *\/  a  *  /   2 + ----- + -------  + 4*\/ 2 *a   *\/  a   - 2*\/ 2 *a *\/  a  *  /   2 + ----- + -------  + 2*\/ 2 *a   *\/  a  *  /   2 + ----- + -------  + 2*\/ 2 *a   *\/  a  *  /   2 + ----- + -------  + 2*2   *a   *\/  a  *  /   2 + ----- + -------  - 2*\/ 2 *a *\/  a  *\/  a  *  /   2 + ----- + -------  - 2*2   *a *\/  a  *\/  a  *  /   2 + ----- + ------- 
                                                                 \/          a        2                                                                                                             \/          a        2                                                 \/          a        2                            \/          a        2                            \/          a        2                           \/          a        2                                  \/          a        2                                 \/          a        2    
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                 4 /      2\                                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                                              2*a *\-2 + a /
2a922a2+2+2aa3+224a922a2+2+2aa44+22a722a2+2+2aa3+2⋅234a722a2+2+2aa44+22a72a3+2⋅234a72a44+4a52a3+424a52a44−234a5a3−2a5a44−224a4a3−22a4a44−224a32a2+2+2aa3a44−22a32a2+2+2aa4−2⋅234a22a2+2+2aa3a44−4a22a2+2+2aa42a4(a2−2)\frac{2 a^{\frac{9}{2}} \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} \sqrt{a^{3}} + 2 \sqrt[4]{2} a^{\frac{9}{2}} \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} \sqrt[4]{a^{4}} + 2 \sqrt{2} a^{\frac{7}{2}} \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} \sqrt{a^{3}} + 2 \cdot 2^{\frac{3}{4}} a^{\frac{7}{2}} \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} \sqrt[4]{a^{4}} + 2 \sqrt{2} a^{\frac{7}{2}} \sqrt{a^{3}} + 2 \cdot 2^{\frac{3}{4}} a^{\frac{7}{2}} \sqrt[4]{a^{4}} + 4 a^{\frac{5}{2}} \sqrt{a^{3}} + 4 \sqrt[4]{2} a^{\frac{5}{2}} \sqrt[4]{a^{4}} - 2^{\frac{3}{4}} a^{5} \sqrt{a^{3}} - 2 a^{5} \sqrt[4]{a^{4}} - 2 \sqrt[4]{2} a^{4} \sqrt{a^{3}} - 2 \sqrt{2} a^{4} \sqrt[4]{a^{4}} - 2 \sqrt[4]{2} a^{3} \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} \sqrt{a^{3}} \sqrt[4]{a^{4}} - 2 \sqrt{2} a^{3} \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} \sqrt{a^{4}} - 2 \cdot 2^{\frac{3}{4}} a^{2} \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} \sqrt{a^{3}} \sqrt[4]{a^{4}} - 4 a^{2} \sqrt{\frac{\sqrt{2} a}{2} + 2 + \frac{\sqrt{2}}{a}} \sqrt{a^{4}}}{2 a^{4} \left(a^{2} - 2\right)} 
(-2*a^5*(a^4)^(1/4) + 4*a^(5/2)*sqrt(a^3) - 2^(3/4)*a^5*sqrt(a^3) - 4*a^2*sqrt(a^4)*sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) - 2*sqrt(2)*a^4*(a^4)^(1/4) - 2*2^(1/4)*a^4*sqrt(a^3) + 2*sqrt(2)*a^(7/2)*sqrt(a^3) + 2*2^(3/4)*a^(7/2)*(a^4)^(1/4) + 2*a^(9/2)*sqrt(a^3)*sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) + 4*2^(1/4)*a^(5/2)*(a^4)^(1/4) - 2*sqrt(2)*a^3*sqrt(a^4)*sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) + 2*sqrt(2)*a^(7/2)*sqrt(a^3)*sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) + 2*2^(1/4)*a^(9/2)*(a^4)^(1/4)*sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) + 2*2^(3/4)*a^(7/2)*(a^4)^(1/4)*sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) - 2*2^(1/4)*a^3*sqrt(a^3)*(a^4)^(1/4)*sqrt(2 + sqrt(2)/a + a*sqrt(2)/2) - 2*2^(3/4)*a^2*sqrt(a^3)*(a^4)^(1/4)*sqrt(2 + sqrt(2)/a + a*sqrt(2)/2))/(2*a^4*(-2 + a^2))
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