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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                1               1           
            b - --          1 - --          
                 2               2          
  ___           b               b        2  
\/ b  - ------------- + ------------- + ----
          ___     1       ___     1      3/2
        \/ b  - -----   \/ b  + -----   b   
                  ___             ___       
                \/ b            \/ b
(1−1b2b+1b+(b−b−1b2b−1b))+2b32\left(\frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} + \left(\sqrt{b} - \frac{b - \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}}\right)\right) + \frac{2}{b^{\frac{3}{2}}} 
sqrt(b) - (b - 1/b^2)/(sqrt(b) - 1/sqrt(b)) + (1 - 1/b^2)/(sqrt(b) + 1/(sqrt(b))) + 2/b^(3/2)
Simplificación general [src] 
0
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0
Descomposición de una fracción [src] 
0
00 
0
Respuesta numérica [src] 
b^0.5 + 2.0*b^(-1.5) + (1.0 - 1/b^2)/(b^0.5 + b^(-0.5)) - (b - 1/b^2)/(b^0.5 - b^(-0.5))
b^0.5 + 2.0*b^(-1.5) + (1.0 - 1/b^2)/(b^0.5 + b^(-0.5)) - (b - 1/b^2)/(b^0.5 - b^(-0.5))
Denominador común [src] 
0
00 
0
Combinatoria [src] 
0
00 
0
Parte trigonométrica [src] 
                       1               1    
                   1 - --          b - --   
                        2               2   
  ___    2             b               b    
\/ b  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        b      \/ b  + -----   \/ b  - -----
                         ___             ___
                       \/ b            \/ b
b+1−1b2b+1b−b−1b2b−1b+2b32\sqrt{b} + \frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} - \frac{b - \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}} + \frac{2}{b^{\frac{3}{2}}} 
sqrt(b) + 2/b^(3/2) + (1 - 1/b^2)/(sqrt(b) + 1/sqrt(b)) - (b - 1/b^2)/(sqrt(b) - 1/sqrt(b))
Denominador racional [src] 
         0          
--------------------
 11                 
b  *(1 + b)*(-1 + b)
0b11(b−1)(b+1)\frac{0}{b^{11} \left(b - 1\right) \left(b + 1\right)} 
0/(b^11*(1 + b)*(-1 + b))
Potencias [src] 
                       1           1        
                   1 - --          -- - b   
                        2           2       
  ___    2             b           b        
\/ b  + ---- + ------------- + -------------
         3/2     ___     1       ___     1  
        b      \/ b  + -----   \/ b  - -----
                         ___             ___
                       \/ b            \/ b
b+1−1b2b+1b+−b+1b2b−1b+2b32\sqrt{b} + \frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} + \frac{- b + \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}} + \frac{2}{b^{\frac{3}{2}}} 
                       1               1    
                   1 - --          b - --   
                        2               2   
  ___    2             b               b    
\/ b  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        b      \/ b  + -----   \/ b  - -----
                         ___             ___
                       \/ b            \/ b
b+1−1b2b+1b−b−1b2b−1b+2b32\sqrt{b} + \frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} - \frac{b - \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}} + \frac{2}{b^{\frac{3}{2}}} 
sqrt(b) + 2/b^(3/2) + (1 - 1/b^2)/(sqrt(b) + 1/sqrt(b)) - (b - 1/b^2)/(sqrt(b) - 1/sqrt(b))
Compilar la expresión [src] 
                       1               1    
                   1 - --          b - --   
                        2               2   
  ___    2             b               b    
\/ b  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        b      \/ b  + -----   \/ b  - -----
                         ___             ___
                       \/ b            \/ b
b+1−1b2b+1b−b−1b2b−1b+2b32\sqrt{b} + \frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} - \frac{b - \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}} + \frac{2}{b^{\frac{3}{2}}} 
sqrt(b) + 2/b^(3/2) + (1 - 1/b^2)/(sqrt(b) + 1/sqrt(b)) - (b - 1/b^2)/(sqrt(b) - 1/sqrt(b))
Unión de expresiones racionales [src] 
        /     3    2         \            /      2\                     
(1 + b)*\1 - b  + b *(-1 + b)/ + (-1 + b)*\-1 + b / + 2*(1 + b)*(-1 + b)
------------------------------------------------------------------------
                          3/2                                           
                         b   *(1 + b)*(-1 + b)
2(b−1)(b+1)+(b−1)(b2−1)+(b+1)(−b3+b2(b−1)+1)b32(b−1)(b+1)\frac{2 \left(b - 1\right) \left(b + 1\right) + \left(b - 1\right) \left(b^{2} - 1\right) + \left(b + 1\right) \left(- b^{3} + b^{2} \left(b - 1\right) + 1\right)}{b^{\frac{3}{2}} \left(b - 1\right) \left(b + 1\right)} 
((1 + b)*(1 - b^3 + b^2*(-1 + b)) + (-1 + b)*(-1 + b^2) + 2*(1 + b)*(-1 + b))/(b^(3/2)*(1 + b)*(-1 + b))
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