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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(a)/(x-48*sqrt(x))/2*sqrt(a)/(48*sqrt(x)-x)

¿Cómo vas a descomponer esta sqrt(a)/(x-48*sqrt(x))/2*sqrt(a)/(48*sqrt(x)-x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
/     ___    \      
|   \/ a     |      
|------------|      
|         ___|      
\x - 48*\/ x /   ___
--------------*\/ a 
      2             
--------------------
         ___        
    48*\/ x  - x
$$\frac{\sqrt{a} \frac{\sqrt{a} \frac{1}{- 48 \sqrt{x} + x}}{2}}{48 \sqrt{x} - x}$$ 
(((sqrt(a)/(x - 48*sqrt(x)))/2)*sqrt(a))/(48*sqrt(x) - x)
Simplificación general [src] 
       -a         
------------------
                 2
  /          ___\ 
2*\-x + 48*\/ x /
$$- \frac{a}{2 \left(48 \sqrt{x} - x\right)^{2}}$$ 
-a/(2*(-x + 48*sqrt(x))^2)
Denominador común [src] 
           -a             
--------------------------
       3/2      2         
- 192*x    + 2*x  + 4608*x
$$- \frac{a}{- 192 x^{\frac{3}{2}} + 2 x^{2} + 4608 x}$$ 
-a/(-192*x^(3/2) + 2*x^2 + 4608*x)
Denominador racional [src] 
                   3/2        2
-4608*a*x - 192*a*x    - 2*a*x 
-------------------------------
 / 2         \ /             2\
 \x  - 2304*x/*\-9216*x + 4*x /
$$\frac{- 192 a x^{\frac{3}{2}} - 2 a x^{2} - 4608 a x}{\left(x^{2} - 2304 x\right) \left(4 x^{2} - 9216 x\right)}$$ 
(-4608*a*x - 192*a*x^(3/2) - 2*a*x^2)/((x^2 - 2304*x)*(-9216*x + 4*x^2))
Potencias [src] 
               a                
--------------------------------
  /         ___\ /          ___\
2*\x - 48*\/ x /*\-x + 48*\/ x /
$$\frac{a}{2 \left(- 48 \sqrt{x} + x\right) \left(48 \sqrt{x} - x\right)}$$ 
       -a         
------------------
                 2
  /          ___\ 
2*\-x + 48*\/ x /
$$- \frac{a}{2 \left(48 \sqrt{x} - x\right)^{2}}$$ 
-a/(2*(-x + 48*sqrt(x))^2)
Respuesta numérica [src] 
0.5*a^1.0/((x - 48.0*x^0.5)*(-x + 48.0*x^0.5))
0.5*a^1.0/((x - 48.0*x^0.5)*(-x + 48.0*x^0.5))
Combinatoria [src] 
       -a        
-----------------
                2
  /         ___\ 
2*\x - 48*\/ x /
$$- \frac{a}{2 \left(- 48 \sqrt{x} + x\right)^{2}}$$ 
-a/(2*(x - 48*sqrt(x))^2)
Compilar la expresión [src] 
               a                
--------------------------------
  /         ___\ /          ___\
2*\x - 48*\/ x /*\-x + 48*\/ x /
$$\frac{a}{2 \left(- 48 \sqrt{x} + x\right) \left(48 \sqrt{x} - x\right)}$$ 
a/(2*(x - 48*sqrt(x))*(-x + 48*sqrt(x)))
Unión de expresiones racionales [src] 
               a                
--------------------------------
  /         ___\ /          ___\
2*\x - 48*\/ x /*\-x + 48*\/ x /
$$\frac{a}{2 \left(- 48 \sqrt{x} + x\right) \left(48 \sqrt{x} - x\right)}$$ 
a/(2*(x - 48*sqrt(x))*(-x + 48*sqrt(x)))
Parte trigonométrica [src] 
               a                
--------------------------------
  /         ___\ /          ___\
2*\x - 48*\/ x /*\-x + 48*\/ x /
$$\frac{a}{2 \left(- 48 \sqrt{x} + x\right) \left(48 \sqrt{x} - x\right)}$$ 
a/(2*(x - 48*sqrt(x))*(-x + 48*sqrt(x)))
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