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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(a)/(x-36*sqrt(x))/9*(a)/(36*sqrt(x)-x)^2

¿Cómo vas a descomponer esta sqrt(a)/(x-36*sqrt(x))/9*(a)/(36*sqrt(x)-x)^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
/     ___    \  
|   \/ a     |  
|------------|  
|         ___|  
\x - 36*\/ x /  
--------------*a
      9         
----------------
              2 
/     ___    \  
\36*\/ x  - x/
aa1−36x+x9(36x−x)2\frac{a \frac{\sqrt{a} \frac{1}{- 36 \sqrt{x} + x}}{9}}{\left(36 \sqrt{x} - x\right)^{2}} 
(((sqrt(a)/(x - 36*sqrt(x)))/9)*a)/(36*sqrt(x) - x)^2
Simplificación general [src] 
        3/2       
      -a          
------------------
                 3
  /          ___\ 
9*\-x + 36*\/ x /
−a329(36x−x)3- \frac{a^{\frac{3}{2}}}{9 \left(36 \sqrt{x} - x\right)^{3}} 
-a^(3/2)/(9*(-x + 36*sqrt(x))^3)
Denominador racional [src] 
                       2                                2
     3/2 /         ___\         3/2   ___ /         ___\ 
9*x*a   *\x + 36*\/ x /  + 324*a   *\/ x *\x + 36*\/ x / 
---------------------------------------------------------
                         2                               
            / 2         \  /                2\           
            \x  - 1296*x/ *\-104976*x + 81*x /
324a32x(36x+x)2+9a32x(36x+x)2(x2−1296x)2(81x2−104976x)\frac{324 a^{\frac{3}{2}} \sqrt{x} \left(36 \sqrt{x} + x\right)^{2} + 9 a^{\frac{3}{2}} x \left(36 \sqrt{x} + x\right)^{2}}{\left(x^{2} - 1296 x\right)^{2} \left(81 x^{2} - 104976 x\right)} 
(9*x*a^(3/2)*(x + 36*sqrt(x))^2 + 324*a^(3/2)*sqrt(x)*(x + 36*sqrt(x))^2)/((x^2 - 1296*x)^2*(-104976*x + 81*x^2))
Compilar la expresión [src] 
                3/2              
               a                 
---------------------------------
                                2
  /         ___\ /          ___\ 
9*\x - 36*\/ x /*\-x + 36*\/ x /
a329(−36x+x)(36x−x)2\frac{a^{\frac{3}{2}}}{9 \left(- 36 \sqrt{x} + x\right) \left(36 \sqrt{x} - x\right)^{2}} 
a^(3/2)/(9*(x - 36*sqrt(x))*(-x + 36*sqrt(x))^2)
Parte trigonométrica [src] 
                3/2              
               a                 
---------------------------------
                                2
  /         ___\ /          ___\ 
9*\x - 36*\/ x /*\-x + 36*\/ x /
a329(−36x+x)(36x−x)2\frac{a^{\frac{3}{2}}}{9 \left(- 36 \sqrt{x} + x\right) \left(36 \sqrt{x} - x\right)^{2}} 
a^(3/2)/(9*(x - 36*sqrt(x))*(-x + 36*sqrt(x))^2)
Potencias [src] 
                3/2              
               a                 
---------------------------------
                                2
  /         ___\ /          ___\ 
9*\x - 36*\/ x /*\-x + 36*\/ x /
a329(−36x+x)(36x−x)2\frac{a^{\frac{3}{2}}}{9 \left(- 36 \sqrt{x} + x\right) \left(36 \sqrt{x} - x\right)^{2}} 
        3/2       
      -a          
------------------
                 3
  /          ___\ 
9*\-x + 36*\/ x /
−a329(36x−x)3- \frac{a^{\frac{3}{2}}}{9 \left(36 \sqrt{x} - x\right)^{3}} 
-a^(3/2)/(9*(-x + 36*sqrt(x))^3)
Combinatoria [src] 
        3/2      
       a         
-----------------
                3
  /         ___\ 
9*\x - 36*\/ x /
a329(−36x+x)3\frac{a^{\frac{3}{2}}}{9 \left(- 36 \sqrt{x} + x\right)^{3}} 
a^(3/2)/(9*(x - 36*sqrt(x))^3)
Unión de expresiones racionales [src] 
                3/2              
               a                 
---------------------------------
                                2
  /         ___\ /          ___\ 
9*\x - 36*\/ x /*\-x + 36*\/ x /
a329(−36x+x)(36x−x)2\frac{a^{\frac{3}{2}}}{9 \left(- 36 \sqrt{x} + x\right) \left(36 \sqrt{x} - x\right)^{2}} 
a^(3/2)/(9*(x - 36*sqrt(x))*(-x + 36*sqrt(x))^2)
Respuesta numérica [src] 
8.57338820301783e-5*a^1.5/((x - 36.0*x^0.5)*(x^0.5 - 0.0277777777777778*x)^2)
8.57338820301783e-5*a^1.5/((x - 36.0*x^0.5)*(x^0.5 - 0.0277777777777778*x)^2)
Denominador común [src] 
                    3/2                   
                   a                      
------------------------------------------
          3/2        5/2      3          2
- 419904*x    - 972*x    + 9*x  + 34992*x
a32−972x52−419904x32+9x3+34992x2\frac{a^{\frac{3}{2}}}{- 972 x^{\frac{5}{2}} - 419904 x^{\frac{3}{2}} + 9 x^{3} + 34992 x^{2}} 
a^(3/2)/(-419904*x^(3/2) - 972*x^(5/2) + 9*x^3 + 34992*x^2)
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