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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(x)/(x-16)-sqrt(x)/((4-sqrt(x))^2)*(m^2-8*m+16)/4*sqrt(m)

¿Cómo vas a descomponer esta sqrt(x)/(x-16)-sqrt(x)/((4-sqrt(x))^2)*(m^2-8*m+16)/4*sqrt(m) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
              ___                          
            \/ x      / 2           \      
         ------------*\m  - 8*m + 16/      
                    2                      
  ___    /      ___\                       
\/ x     \4 - \/ x /                    ___
------ - ----------------------------*\/ m 
x - 16                4
−mx(4−x)2((m2−8m)+16)4+xx−16- \sqrt{m} \frac{\frac{\sqrt{x}}{\left(4 - \sqrt{x}\right)^{2}} \left(\left(m^{2} - 8 m\right) + 16\right)}{4} + \frac{\sqrt{x}}{x - 16} 
sqrt(x)/(x - 16) - ((sqrt(x)/(4 - sqrt(x))^2)*(m^2 - 8*m + 16))/4*sqrt(m)
Simplificación general [src] 
      /            2     ___           /      2      \\
  ___ |/       ___\    \/ m *(-16 + x)*\16 + m  - 8*m/|
\/ x *|\-4 + \/ x /  - -------------------------------|
      \                               4               /
-------------------------------------------------------
                                      2                
                          /       ___\                 
                (-16 + x)*\-4 + \/ x /
x(−m(x−16)(m2−8m+16)4+(x−4)2)(x−4)2(x−16)\frac{\sqrt{x} \left(- \frac{\sqrt{m} \left(x - 16\right) \left(m^{2} - 8 m + 16\right)}{4} + \left(\sqrt{x} - 4\right)^{2}\right)}{\left(\sqrt{x} - 4\right)^{2} \left(x - 16\right)} 
sqrt(x)*((-4 + sqrt(x))^2 - sqrt(m)*(-16 + x)*(16 + m^2 - 8*m)/4)/((-16 + x)*(-4 + sqrt(x))^2)
Potencias [src] 
                      /            2\
            ___   ___ |           m |
   ___    \/ m *\/ x *|-4 + 2*m - --|
 \/ x                 \           4 /
------- + ---------------------------
-16 + x                      2       
                  /      ___\        
                  \4 - \/ x /
mx(−m24+2m−4)(4−x)2+xx−16\frac{\sqrt{m} \sqrt{x} \left(- \frac{m^{2}}{4} + 2 m - 4\right)}{\left(4 - \sqrt{x}\right)^{2}} + \frac{\sqrt{x}}{x - 16} 
                  /            2\
            _____ |           m |
   ___    \/ m*x *|-4 + 2*m - --|
 \/ x             \           4 /
------- + -----------------------
-16 + x                    2     
                /      ___\      
                \4 - \/ x /
xx−16+mx(−m24+2m−4)(4−x)2\frac{\sqrt{x}}{x - 16} + \frac{\sqrt{m x} \left(- \frac{m^{2}}{4} + 2 m - 4\right)}{\left(4 - \sqrt{x}\right)^{2}} 
   ___      ___   ___ /      2      \
 \/ x     \/ m *\/ x *\16 + m  - 8*m/
------- - ---------------------------
-16 + x                       2      
                   /      ___\       
                 4*\4 - \/ x /
−mx(m2−8m+16)4(4−x)2+xx−16- \frac{\sqrt{m} \sqrt{x} \left(m^{2} - 8 m + 16\right)}{4 \left(4 - \sqrt{x}\right)^{2}} + \frac{\sqrt{x}}{x - 16} 
sqrt(x)/(-16 + x) - sqrt(m)*sqrt(x)*(16 + m^2 - 8*m)/(4*(4 - sqrt(x))^2)
Respuesta numérica [src] 
x^0.5/(-16.0 + x) - 0.015625*m^0.5*x^0.5*(16.0 + m^2 - 8.0*m)/(1 - 0.25*x^0.5)^2
x^0.5/(-16.0 + x) - 0.015625*m^0.5*x^0.5*(16.0 + m^2 - 8.0*m)/(1 - 0.25*x^0.5)^2
Unión de expresiones racionales [src] 
      /             2                                    \
  ___ |  /      ___\      ___                            |
\/ x *\4*\4 - \/ x /  - \/ m *(-16 + x)*(16 + m*(-8 + m))/
----------------------------------------------------------
                                        2                 
                             /      ___\                  
                 4*(-16 + x)*\4 - \/ x /
x(−m(x−16)(m(m−8)+16)+4(4−x)2)4(4−x)2(x−16)\frac{\sqrt{x} \left(- \sqrt{m} \left(x - 16\right) \left(m \left(m - 8\right) + 16\right) + 4 \left(4 - \sqrt{x}\right)^{2}\right)}{4 \left(4 - \sqrt{x}\right)^{2} \left(x - 16\right)} 
sqrt(x)*(4*(4 - sqrt(x))^2 - sqrt(m)*(-16 + x)*(16 + m*(-8 + m)))/(4*(-16 + x)*(4 - sqrt(x))^2)
Denominador racional [src] 
                       2                             2                            2                       2            2                          2                            2                              2
   5/2  3/2 /      ___\         3/2   ___ /      ___\         ___  3/2 /      ___\        ___ /       ___\  /      ___\       3/2  3/2 /      ___\        5/2   ___ /      ___\          ___   ___ /      ___\ 
- m   *x   *\4 + \/ x /  - 128*m   *\/ x *\4 + \/ x /  - 16*\/ m *x   *\4 + \/ x /  + 4*\/ x *\-4 + \/ x / *\4 + \/ x /  + 8*m   *x   *\4 + \/ x /  + 16*m   *\/ x *\4 + \/ x /  + 256*\/ m *\/ x *\4 + \/ x / 
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                             3                                                                                                 
                                                                                                  4*(-16 + x)
−m52x32(x+4)2+16m52x(x+4)2+8m32x32(x+4)2−128m32x(x+4)2−16mx32(x+4)2+256mx(x+4)2+4x(x−4)2(x+4)24(x−16)3\frac{- m^{\frac{5}{2}} x^{\frac{3}{2}} \left(\sqrt{x} + 4\right)^{2} + 16 m^{\frac{5}{2}} \sqrt{x} \left(\sqrt{x} + 4\right)^{2} + 8 m^{\frac{3}{2}} x^{\frac{3}{2}} \left(\sqrt{x} + 4\right)^{2} - 128 m^{\frac{3}{2}} \sqrt{x} \left(\sqrt{x} + 4\right)^{2} - 16 \sqrt{m} x^{\frac{3}{2}} \left(\sqrt{x} + 4\right)^{2} + 256 \sqrt{m} \sqrt{x} \left(\sqrt{x} + 4\right)^{2} + 4 \sqrt{x} \left(\sqrt{x} - 4\right)^{2} \left(\sqrt{x} + 4\right)^{2}}{4 \left(x - 16\right)^{3}} 
(-m^(5/2)*x^(3/2)*(4 + sqrt(x))^2 - 128*m^(3/2)*sqrt(x)*(4 + sqrt(x))^2 - 16*sqrt(m)*x^(3/2)*(4 + sqrt(x))^2 + 4*sqrt(x)*(-4 + sqrt(x))^2*(4 + sqrt(x))^2 + 8*m^(3/2)*x^(3/2)*(4 + sqrt(x))^2 + 16*m^(5/2)*sqrt(x)*(4 + sqrt(x))^2 + 256*sqrt(m)*sqrt(x)*(4 + sqrt(x))^2)/(4*(-16 + x)^3)
Compilar la expresión [src] 
      /            ___ /      2      \\
  ___ |   1      \/ m *\16 + m  - 8*m/|
\/ x *|------- - ---------------------|
      |-16 + x                    2   |
      |                /      ___\    |
      \              4*\4 - \/ x /    /
x(−m(m2−8m+16)4(4−x)2+1x−16)\sqrt{x} \left(- \frac{\sqrt{m} \left(m^{2} - 8 m + 16\right)}{4 \left(4 - \sqrt{x}\right)^{2}} + \frac{1}{x - 16}\right) 
   ___      ___   ___ /      2      \
 \/ x     \/ m *\/ x *\16 + m  - 8*m/
------- - ---------------------------
-16 + x                       2      
                   /      ___\       
                 4*\4 - \/ x /
−mx(m2−8m+16)4(4−x)2+xx−16- \frac{\sqrt{m} \sqrt{x} \left(m^{2} - 8 m + 16\right)}{4 \left(4 - \sqrt{x}\right)^{2}} + \frac{\sqrt{x}}{x - 16} 
sqrt(x)/(-16 + x) - sqrt(m)*sqrt(x)*(16 + m^2 - 8*m)/(4*(4 - sqrt(x))^2)
Parte trigonométrica [src] 
   ___      ___   ___ /      2      \
 \/ x     \/ m *\/ x *\16 + m  - 8*m/
------- - ---------------------------
-16 + x                       2      
                   /      ___\       
                 4*\4 - \/ x /
−mx(m2−8m+16)4(4−x)2+xx−16- \frac{\sqrt{m} \sqrt{x} \left(m^{2} - 8 m + 16\right)}{4 \left(4 - \sqrt{x}\right)^{2}} + \frac{\sqrt{x}}{x - 16} 
sqrt(x)/(-16 + x) - sqrt(m)*sqrt(x)*(16 + m^2 - 8*m)/(4*(4 - sqrt(x))^2)
Denominador común [src] 
 /       ___      3/2           5/2  3/2         ___   ___       5/2   ___      3/2  3/2        ___  3/2        3/2   ___\ 
-\- 64*\/ x  - 4*x    + 32*x + m   *x    - 256*\/ m *\/ x  - 16*m   *\/ x  - 8*m   *x    + 16*\/ m *x    + 128*m   *\/ x / 
---------------------------------------------------------------------------------------------------------------------------
                                                         3/2      2         ___                                            
                                             -1024 - 32*x    + 4*x  + 512*\/ x
−m52x32−16m52x−8m32x32+128m32x+16mx32−256mx−4x32−64x+32x−32x32+512x+4x2−1024- \frac{m^{\frac{5}{2}} x^{\frac{3}{2}} - 16 m^{\frac{5}{2}} \sqrt{x} - 8 m^{\frac{3}{2}} x^{\frac{3}{2}} + 128 m^{\frac{3}{2}} \sqrt{x} + 16 \sqrt{m} x^{\frac{3}{2}} - 256 \sqrt{m} \sqrt{x} - 4 x^{\frac{3}{2}} - 64 \sqrt{x} + 32 x}{- 32 x^{\frac{3}{2}} + 512 \sqrt{x} + 4 x^{2} - 1024} 
-(-64*sqrt(x) - 4*x^(3/2) + 32*x + m^(5/2)*x^(3/2) - 256*sqrt(m)*sqrt(x) - 16*m^(5/2)*sqrt(x) - 8*m^(3/2)*x^(3/2) + 16*sqrt(m)*x^(3/2) + 128*m^(3/2)*sqrt(x))/(-1024 - 32*x^(3/2) + 4*x^2 + 512*sqrt(x))
Combinatoria [src] 
   ___ /            ___       5/2              ___        3/2      5/2        3/2          ___\ 
-\/ x *\-64 - 256*\/ m  - 16*m    - 4*x + 32*\/ x  + 128*m    + x*m    - 8*x*m    + 16*x*\/ m / 
------------------------------------------------------------------------------------------------
                                                           2                                    
                                               /       ___\                                     
                                   4*(-16 + x)*\-4 + \/ x /
−x(m52x−16m52−8m32x+128m32+16mx−256m+32x−4x−64)4(x−4)2(x−16)- \frac{\sqrt{x} \left(m^{\frac{5}{2}} x - 16 m^{\frac{5}{2}} - 8 m^{\frac{3}{2}} x + 128 m^{\frac{3}{2}} + 16 \sqrt{m} x - 256 \sqrt{m} + 32 \sqrt{x} - 4 x - 64\right)}{4 \left(\sqrt{x} - 4\right)^{2} \left(x - 16\right)} 
-sqrt(x)*(-64 - 256*sqrt(m) - 16*m^(5/2) - 4*x + 32*sqrt(x) + 128*m^(3/2) + x*m^(5/2) - 8*x*m^(3/2) + 16*x*sqrt(m))/(4*(-16 + x)*(-4 + sqrt(x))^2)
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