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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(x*sqrt(a)/(5*x-3)^4)*(5*x-3)^4*(sqrt(a)/(2*(5*x-3)^4)-10*x*sqrt(a)/(5*x-3)^5)/(sqrt(a)*x)

¿Cómo vas a descomponer esta sqrt(x*sqrt(a)/(5*x-3)^4)*(5*x-3)^4*(sqrt(a)/(2*(5*x-3)^4)-10*x*sqrt(a)/(5*x-3)^5)/(sqrt(a)*x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
      ____________                                       
     /      ___               /     ___              ___\
    /   x*\/ a              4 |   \/ a        10*x*\/ a |
   /   ---------- *(5*x - 3) *|------------ - ----------|
  /             4             |           4            5|
\/     (5*x - 3)              \2*(5*x - 3)    (5*x - 3) /
---------------------------------------------------------
                           ___                           
                         \/ a *x
ax(5x−3)4(5x−3)4(a2(5x−3)4−a10x(5x−3)5)ax\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(\frac{\sqrt{a}}{2 \left(5 x - 3\right)^{4}} - \frac{\sqrt{a} 10 x}{\left(5 x - 3\right)^{5}}\right)}{\sqrt{a} x} 
((sqrt((x*sqrt(a))/(5*x - 3)^4)*(5*x - 3)^4)*(sqrt(a)/((2*(5*x - 3)^4)) - (10*x)*sqrt(a)/(5*x - 3)^5))/((sqrt(a)*x))
Simplificación general [src] 
         _____________          
        /       ___             
       /    x*\/ a              
-3*   /   ----------- *(1 + 5*x)
     /              4           
   \/     (-3 + 5*x)            
--------------------------------
         2*x*(-3 + 5*x)
−3ax(5x−3)4(5x+1)2x(5x−3)- \frac{3 \sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x + 1\right)}{2 x \left(5 x - 3\right)} 
-3*sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(1 + 5*x)/(2*x*(-3 + 5*x))
Respuesta numérica [src] 
25.0*a^(-0.5)*(x*a^0.5/(-0.6 + x)^4)^0.5*(-0.6 + x)^4*(0.0008*a^0.5/(-0.6 + x)^4 - 0.0032*x*a^0.5/(-0.6 + x)^5)/x
25.0*a^(-0.5)*(x*a^0.5/(-0.6 + x)^4)^0.5*(-0.6 + x)^4*(0.0008*a^0.5/(-0.6 + x)^4 - 0.0032*x*a^0.5/(-0.6 + x)^5)/x
Abrimos la expresión [src] 
     ____________    _________            /     ___              ___\
    /     1         /     ___           4 |   \/ a        10*x*\/ a |
   /  ---------- *\/  x*\/ a  *(5*x - 3) *|------------ - ----------|
  /            4                          |           4            5|
\/    (5*x - 3)                           \2*(5*x - 3)    (5*x - 3) /
---------------------------------------------------------------------
                                 ___                                 
                               \/ a *x
ax(5x−3)4(a2(5x−3)4−a10x(5x−3)5)1(5x−3)4ax\frac{\sqrt{\sqrt{a} x} \left(5 x - 3\right)^{4} \left(\frac{\sqrt{a}}{2 \left(5 x - 3\right)^{4}} - \frac{\sqrt{a} 10 x}{\left(5 x - 3\right)^{5}}\right) \sqrt{\frac{1}{\left(5 x - 3\right)^{4}}}}{\sqrt{a} x} 
sqrt(1/((5*x - 3)^4))*sqrt(x*sqrt(a))*(5*x - 3)^4*(sqrt(a)/(2*(5*x - 3)^4) - (10*x)*sqrt(a)/(5*x - 3)^5)/(sqrt(a)*x)
Denominador común [src] 
 /        _________________________________________              _________________________________________\ 
 |       /                     ___                              /                     ___                 | 
 |      /                  x*\/ a                              /                  x*\/ a                  | 
-|3*   /   ---------------------------------------  + 15*x*   /   --------------------------------------- | 
 |    /               3                4         2           /               3                4         2 | 
 \  \/     81 - 1500*x  - 540*x + 625*x  + 1350*x          \/     81 - 1500*x  - 540*x + 625*x  + 1350*x  / 
------------------------------------------------------------------------------------------------------------
                                                           2                                                
                                                -6*x + 10*x
−15xax625x4−1500x3+1350x2−540x+81+3ax625x4−1500x3+1350x2−540x+8110x2−6x- \frac{15 x \sqrt{\frac{\sqrt{a} x}{625 x^{4} - 1500 x^{3} + 1350 x^{2} - 540 x + 81}} + 3 \sqrt{\frac{\sqrt{a} x}{625 x^{4} - 1500 x^{3} + 1350 x^{2} - 540 x + 81}}}{10 x^{2} - 6 x} 
-(3*sqrt(x*sqrt(a)/(81 - 1500*x^3 - 540*x + 625*x^4 + 1350*x^2)) + 15*x*sqrt(x*sqrt(a)/(81 - 1500*x^3 - 540*x + 625*x^4 + 1350*x^2)))/(-6*x + 10*x^2)
Unión de expresiones racionales [src] 
        _____________           
       /       ___              
      /    x*\/ a               
3*   /   ----------- *(-1 - 5*x)
    /              4            
  \/     (-3 + 5*x)             
--------------------------------
         2*x*(-3 + 5*x)
3ax(5x−3)4(−5x−1)2x(5x−3)\frac{3 \sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(- 5 x - 1\right)}{2 x \left(5 x - 3\right)} 
3*sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(-1 - 5*x)/(2*x*(-3 + 5*x))
Parte trigonométrica [src] 
      _____________                                          
     /       ___                /      ___               ___\
    /    x*\/ a               4 |    \/ a         10*x*\/ a |
   /   ----------- *(-3 + 5*x) *|------------- - -----------|
  /              4              |            4             5|
\/     (-3 + 5*x)               \2*(-3 + 5*x)    (-3 + 5*x) /
-------------------------------------------------------------
                             ___                             
                           \/ a *x
ax(5x−3)4(5x−3)4(−10ax(5x−3)5+a2(5x−3)4)ax\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(- \frac{10 \sqrt{a} x}{\left(5 x - 3\right)^{5}} + \frac{\sqrt{a}}{2 \left(5 x - 3\right)^{4}}\right)}{\sqrt{a} x} 
sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(-3 + 5*x)^4*(sqrt(a)/(2*(-3 + 5*x)^4) - 10*x*sqrt(a)/(-3 + 5*x)^5)/(sqrt(a)*x)
Potencias [src] 
      _____________                                          
     /       ___                /      ___               ___\
    /    x*\/ a               4 |    \/ a         10*x*\/ a |
   /   ----------- *(-3 + 5*x) *|------------- - -----------|
  /              4              |            4             5|
\/     (-3 + 5*x)               \2*(-3 + 5*x)    (-3 + 5*x) /
-------------------------------------------------------------
                             ___                             
                           \/ a *x
ax(5x−3)4(5x−3)4(−10ax(5x−3)5+a2(5x−3)4)ax\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(- \frac{10 \sqrt{a} x}{\left(5 x - 3\right)^{5}} + \frac{\sqrt{a}}{2 \left(5 x - 3\right)^{4}}\right)}{\sqrt{a} x} 
sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(-3 + 5*x)^4*(sqrt(a)/(2*(-3 + 5*x)^4) - 10*x*sqrt(a)/(-3 + 5*x)^5)/(sqrt(a)*x)
Combinatoria [src] 
         _________________________________________          
        /                     ___                           
       /                  x*\/ a                            
-3*   /   --------------------------------------- *(1 + 5*x)
     /               3                4         2           
   \/     81 - 1500*x  - 540*x + 625*x  + 1350*x            
------------------------------------------------------------
                       2*x*(-3 + 5*x)
−3ax625x4−1500x3+1350x2−540x+81(5x+1)2x(5x−3)- \frac{3 \sqrt{\frac{\sqrt{a} x}{625 x^{4} - 1500 x^{3} + 1350 x^{2} - 540 x + 81}} \left(5 x + 1\right)}{2 x \left(5 x - 3\right)} 
-3*sqrt(x*sqrt(a)/(81 - 1500*x^3 - 540*x + 625*x^4 + 1350*x^2))*(1 + 5*x)/(2*x*(-3 + 5*x))
Denominador racional [src] 
            ____________                                ____________            
           /      ___                                  /      ___               
  ___     /   x*\/ a               5          ___     /   x*\/ a               4
\/ a *   /   ---------- *(-3 + 5*x)  - 20*x*\/ a *   /   ---------- *(-3 + 5*x) 
        /             4                             /             4             
      \/     (5*x - 3)                            \/     (5*x - 3)              
--------------------------------------------------------------------------------
                                 ___             5                              
                             2*\/ a *x*(-3 + 5*x)
−20axax(5x−3)4(5x−3)4+aax(5x−3)4(5x−3)52ax(5x−3)5\frac{- 20 \sqrt{a} x \sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} + \sqrt{a} \sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{5}}{2 \sqrt{a} x \left(5 x - 3\right)^{5}} 
(sqrt(a)*sqrt(x*sqrt(a)/(5*x - 3)^4)*(-3 + 5*x)^5 - 20*x*sqrt(a)*sqrt(x*sqrt(a)/(5*x - 3)^4)*(-3 + 5*x)^4)/(2*sqrt(a)*x*(-3 + 5*x)^5)
Compilar la expresión [src] 
      _____________                                          
     /       ___                /      ___               ___\
    /    x*\/ a               4 |    \/ a         10*x*\/ a |
   /   ----------- *(-3 + 5*x) *|------------- - -----------|
  /              4              |            4             5|
\/     (-3 + 5*x)               \2*(-3 + 5*x)    (-3 + 5*x) /
-------------------------------------------------------------
                             ___                             
                           \/ a *x
ax(5x−3)4(5x−3)4(−10ax(5x−3)5+a2(5x−3)4)ax\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(- \frac{10 \sqrt{a} x}{\left(5 x - 3\right)^{5}} + \frac{\sqrt{a}}{2 \left(5 x - 3\right)^{4}}\right)}{\sqrt{a} x} 
      _____________                                          
     /       ___                                             
    /    x*\/ a               4 /      1             10*x   \
   /   ----------- *(-3 + 5*x) *|------------- - -----------|
  /              4              |            4             5|
\/     (-3 + 5*x)               \2*(-3 + 5*x)    (-3 + 5*x) /
-------------------------------------------------------------
                              x
ax(5x−3)4(5x−3)4(−10x(5x−3)5+12(5x−3)4)x\frac{\sqrt{\frac{\sqrt{a} x}{\left(5 x - 3\right)^{4}}} \left(5 x - 3\right)^{4} \left(- \frac{10 x}{\left(5 x - 3\right)^{5}} + \frac{1}{2 \left(5 x - 3\right)^{4}}\right)}{x} 
sqrt(x*sqrt(a)/(-3 + 5*x)^4)*(-3 + 5*x)^4*(1/(2*(-3 + 5*x)^4) - 10*x/(-3 + 5*x)^5)/x
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