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¿Cómo vas a descomponer esta sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
                1               1           
            a - --          1 - --          
                 2               2          
  ___           a               a        2  
\/ a  - ------------- + ------------- + ----
          ___     1       ___     1      3/2
        \/ a  - -----   \/ a  + -----   a   
                  ___             ___       
                \/ a            \/ a        
$$\left(\frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} + \left(\sqrt{a} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}}\right)\right) + \frac{2}{a^{\frac{3}{2}}}$$
sqrt(a) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a)) + (1 - 1/a^2)/(sqrt(a) + 1/(sqrt(a))) + 2/a^(3/2)
Descomposición de una fracción [src]
0
$$0$$
0
Simplificación general [src]
0
$$0$$
0
Denominador común [src]
0
$$0$$
0
Potencias [src]
                       1               1    
                   1 - --          a - --   
                        2               2   
  ___    2             a               a    
\/ a  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        a      \/ a  + -----   \/ a  - -----
                         ___             ___
                       \/ a            \/ a 
$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$
                       1           1        
                   1 - --          -- - a   
                        2           2       
  ___    2             a           a        
\/ a  + ---- + ------------- + -------------
         3/2     ___     1       ___     1  
        a      \/ a  + -----   \/ a  - -----
                         ___             ___
                       \/ a            \/ a 
$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} + \frac{- a + \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$
sqrt(a) + 2/a^(3/2) + (1 - 1/a^2)/(sqrt(a) + 1/sqrt(a)) + (a^(-2) - a)/(sqrt(a) - 1/sqrt(a))
Denominador racional [src]
         0          
--------------------
 11                 
a  *(1 + a)*(-1 + a)
$$\frac{0}{a^{11} \left(a - 1\right) \left(a + 1\right)}$$
0/(a^11*(1 + a)*(-1 + a))
Combinatoria [src]
0
$$0$$
0
Respuesta numérica [src]
a^0.5 + 2.0*a^(-1.5) + (1.0 - 1/a^2)/(a^0.5 + a^(-0.5)) - (a - 1/a^2)/(a^0.5 - a^(-0.5))
a^0.5 + 2.0*a^(-1.5) + (1.0 - 1/a^2)/(a^0.5 + a^(-0.5)) - (a - 1/a^2)/(a^0.5 - a^(-0.5))
Unión de expresiones racionales [src]
        /     3    2         \            /      2\                     
(1 + a)*\1 - a  + a *(-1 + a)/ + (-1 + a)*\-1 + a / + 2*(1 + a)*(-1 + a)
------------------------------------------------------------------------
                          3/2                                           
                         a   *(1 + a)*(-1 + a)                          
$$\frac{2 \left(a - 1\right) \left(a + 1\right) + \left(a - 1\right) \left(a^{2} - 1\right) + \left(a + 1\right) \left(- a^{3} + a^{2} \left(a - 1\right) + 1\right)}{a^{\frac{3}{2}} \left(a - 1\right) \left(a + 1\right)}$$
((1 + a)*(1 - a^3 + a^2*(-1 + a)) + (-1 + a)*(-1 + a^2) + 2*(1 + a)*(-1 + a))/(a^(3/2)*(1 + a)*(-1 + a))
Parte trigonométrica [src]
                       1               1    
                   1 - --          a - --   
                        2               2   
  ___    2             a               a    
\/ a  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        a      \/ a  + -----   \/ a  - -----
                         ___             ___
                       \/ a            \/ a 
$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$
sqrt(a) + 2/a^(3/2) + (1 - 1/a^2)/(sqrt(a) + 1/sqrt(a)) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a))
Compilar la expresión [src]
                       1               1    
                   1 - --          a - --   
                        2               2   
  ___    2             a               a    
\/ a  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        a      \/ a  + -----   \/ a  - -----
                         ___             ___
                       \/ a            \/ a 
$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$
sqrt(a) + 2/a^(3/2) + (1 - 1/a^2)/(sqrt(a) + 1/sqrt(a)) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a))