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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(x)/(m-16)-sqrt(m)/(4-sqrt(m))^2

¿Cómo vas a descomponer esta sqrt(x)/(m-16)-sqrt(m)/(4-sqrt(m))^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  ___         ___    
\/ x        \/ m     
------ - ------------
m - 16              2
         /      ___\ 
         \4 - \/ m /
−m(4−m)2+xm−16- \frac{\sqrt{m}}{\left(4 - \sqrt{m}\right)^{2}} + \frac{\sqrt{x}}{m - 16} 
sqrt(x)/(m - 16) - sqrt(m)/(4 - sqrt(m))^2
Simplificación general [src] 
                                   2
  ___              ___ /       ___\ 
\/ m *(16 - m) + \/ x *\-4 + \/ m / 
------------------------------------
                            2       
                /       ___\        
      (-16 + m)*\-4 + \/ m /
m(16−m)+x(m−4)2(m−4)2(m−16)\frac{\sqrt{m} \left(16 - m\right) + \sqrt{x} \left(\sqrt{m} - 4\right)^{2}}{\left(\sqrt{m} - 4\right)^{2} \left(m - 16\right)} 
(sqrt(m)*(16 - m) + sqrt(x)*(-4 + sqrt(m))^2)/((-16 + m)*(-4 + sqrt(m))^2)
Respuesta numérica [src] 
x^0.5/(-16.0 + m) - 0.0625*m^0.5/(1 - 0.25*m^0.5)^2
x^0.5/(-16.0 + m) - 0.0625*m^0.5/(1 - 0.25*m^0.5)^2
Denominador racional [src] 
                  2                       2                     2            2
   3/2 /      ___\         ___ /      ___\      ___ /       ___\  /      ___\ 
- m   *\4 + \/ m /  + 16*\/ m *\4 + \/ m /  + \/ x *\-4 + \/ m / *\4 + \/ m / 
------------------------------------------------------------------------------
                                           3                                  
                                  (-16 + m)
−m32(m+4)2+16m(m+4)2+x(m−4)2(m+4)2(m−16)3\frac{- m^{\frac{3}{2}} \left(\sqrt{m} + 4\right)^{2} + 16 \sqrt{m} \left(\sqrt{m} + 4\right)^{2} + \sqrt{x} \left(\sqrt{m} - 4\right)^{2} \left(\sqrt{m} + 4\right)^{2}}{\left(m - 16\right)^{3}} 
(-m^(3/2)*(4 + sqrt(m))^2 + 16*sqrt(m)*(4 + sqrt(m))^2 + sqrt(x)*(-4 + sqrt(m))^2*(4 + sqrt(m))^2)/(-16 + m)^3
Combinatoria [src] 
   3/2        ___        ___       ___       ___   ___
- m    + 16*\/ m  + 16*\/ x  + m*\/ x  - 8*\/ m *\/ x 
------------------------------------------------------
                                     2                
                         /       ___\                 
               (-16 + m)*\-4 + \/ m /
−m32−8mx+16m+mx+16x(m−4)2(m−16)\frac{- m^{\frac{3}{2}} - 8 \sqrt{m} \sqrt{x} + 16 \sqrt{m} + m \sqrt{x} + 16 \sqrt{x}}{\left(\sqrt{m} - 4\right)^{2} \left(m - 16\right)} 
(-m^(3/2) + 16*sqrt(m) + 16*sqrt(x) + m*sqrt(x) - 8*sqrt(m)*sqrt(x))/((-16 + m)*(-4 + sqrt(m))^2)
Unión de expresiones racionales [src] 
                 2                  
  ___ /      ___\      ___          
\/ x *\4 - \/ m /  - \/ m *(-16 + m)
------------------------------------
                            2       
                 /      ___\        
       (-16 + m)*\4 - \/ m /
−m(m−16)+x(4−m)2(4−m)2(m−16)\frac{- \sqrt{m} \left(m - 16\right) + \sqrt{x} \left(4 - \sqrt{m}\right)^{2}}{\left(4 - \sqrt{m}\right)^{2} \left(m - 16\right)} 
(sqrt(x)*(4 - sqrt(m))^2 - sqrt(m)*(-16 + m))/((-16 + m)*(4 - sqrt(m))^2)
Denominador común [src] 
   3/2        ___        ___       ___       ___   ___
- m    + 16*\/ m  + 16*\/ x  + m*\/ x  - 8*\/ m *\/ x 
------------------------------------------------------
                    2      3/2         ___            
            -256 + m  - 8*m    + 128*\/ m
−m32−8mx+16m+mx+16x−8m32+128m+m2−256\frac{- m^{\frac{3}{2}} - 8 \sqrt{m} \sqrt{x} + 16 \sqrt{m} + m \sqrt{x} + 16 \sqrt{x}}{- 8 m^{\frac{3}{2}} + 128 \sqrt{m} + m^{2} - 256} 
(-m^(3/2) + 16*sqrt(m) + 16*sqrt(x) + m*sqrt(x) - 8*sqrt(m)*sqrt(x))/(-256 + m^2 - 8*m^(3/2) + 128*sqrt(m))
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