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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(m)/((m-16))-sqrt(m)/(((4-sqrt(m))^2))еслиm=1/3

¿Cómo vas a descomponer esta sqrt(m)/((m-16))-sqrt(m)/(((4-sqrt(m))^2))еслиm=1/3 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  ___         ___    
\/ m        \/ m     
------ - ------------
m - 16              2
         /      ___\ 
         \4 - \/ m /
mm−16−m(4−m)2\frac{\sqrt{m}}{m - 16} - \frac{\sqrt{m}}{\left(4 - \sqrt{m}\right)^{2}} 
sqrt(m)/(m - 16) - sqrt(m)/(4 - sqrt(m))^2
Simplificación general [src] 
      /                 2    \
  ___ |     /       ___\     |
\/ m *\16 + \-4 + \/ m /  - m/
------------------------------
                         2    
             /       ___\     
   (-16 + m)*\-4 + \/ m /
m(−m+(m−4)2+16)(m−4)2(m−16)\frac{\sqrt{m} \left(- m + \left(\sqrt{m} - 4\right)^{2} + 16\right)}{\left(\sqrt{m} - 4\right)^{2} \left(m - 16\right)} 
sqrt(m)*(16 + (-4 + sqrt(m))^2 - m)/((-16 + m)*(-4 + sqrt(m))^2)
Sustitución de una condición [src] 
sqrt(m)/(m - 16) - sqrt(m)/(4 - sqrt(m))^2 con m = 1/3
sqrt(m)/(m - 16) - sqrt(m)/(4 - sqrt(m))^2
mm−16−m(4−m)2\frac{\sqrt{m}}{m - 16} - \frac{\sqrt{m}}{\left(4 - \sqrt{m}\right)^{2}} 
sqrt((1/3))/((1/3) - 16) - sqrt((1/3))/(4 - sqrt((1/3)))^2
(1/3)(1/3)−16−(1/3)(4−(1/3))2\frac{\sqrt{(1/3)}}{(1/3) - 16} - \frac{\sqrt{(1/3)}}{\left(4 - \sqrt{(1/3)}\right)^{2}} 
sqrt(1/3)/(1/3 - 16) - sqrt(1/3)/(4 - sqrt(1/3))^2
−13(4−13)2+13(−16+13)- \frac{1}{\sqrt{3} \left(4 - \sqrt{\frac{1}{3}}\right)^{2}} + \frac{1}{\sqrt{3} \left(-16 + \frac{1}{3}\right)} 
-sqrt(3)/47 - sqrt(3)/(3*(4 - sqrt(3)/3)^2)
−33(4−33)2−347- \frac{\sqrt{3}}{3 \left(4 - \frac{\sqrt{3}}{3}\right)^{2}} - \frac{\sqrt{3}}{47} 
    ___         ___     
  \/ 3        \/ 3      
- ----- - --------------
    47                 2
            /      ___\ 
            |    \/ 3 | 
          3*|4 - -----| 
            \      3  /
Respuesta numérica [src] 
m^0.5/(-16.0 + m) - 0.0625*m^0.5/(1 - 0.25*m^0.5)^2
m^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 /  + \/ m *\-4 + \/ m / *\4 + \/ m / 
------------------------------------------------------------------------------
                                           3                                  
                                  (-16 + m)
−m32(m+4)2+m(m−4)2(m+4)2+16m(m+4)2(m−16)3\frac{- m^{\frac{3}{2}} \left(\sqrt{m} + 4\right)^{2} + \sqrt{m} \left(\sqrt{m} - 4\right)^{2} \left(\sqrt{m} + 4\right)^{2} + 16 \sqrt{m} \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(m)*(-4 + sqrt(m))^2*(4 + sqrt(m))^2)/(-16 + m)^3
Unión de expresiones racionales [src] 
      /                2    \
  ___ |     /      ___\     |
\/ m *\16 + \4 - \/ m /  - m/
-----------------------------
                         2   
              /      ___\    
    (-16 + m)*\4 - \/ m /
m(−m+(4−m)2+16)(4−m)2(m−16)\frac{\sqrt{m} \left(- m + \left(4 - \sqrt{m}\right)^{2} + 16\right)}{\left(4 - \sqrt{m}\right)^{2} \left(m - 16\right)} 
sqrt(m)*(16 + (4 - sqrt(m))^2 - m)/((-16 + m)*(4 - sqrt(m))^2)
Combinatoria [src] 
            ___       
       -8*\/ m        
----------------------
          /       ___\
(-16 + m)*\-4 + \/ m /
−8m(m−4)(m−16)- \frac{8 \sqrt{m}}{\left(\sqrt{m} - 4\right) \left(m - 16\right)} 
-8*sqrt(m)/((-16 + m)*(-4 + sqrt(m)))
Denominador común [src] 
      /       ___      \      
     -\- 32*\/ m  + 8*m/      
------------------------------
        2      3/2         ___
-256 + m  - 8*m    + 128*\/ m
−−32m+8m−8m32+128m+m2−256- \frac{- 32 \sqrt{m} + 8 m}{- 8 m^{\frac{3}{2}} + 128 \sqrt{m} + m^{2} - 256} 
-(-32*sqrt(m) + 8*m)/(-256 + m^2 - 8*m^(3/2) + 128*sqrt(m))
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