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¿Cómo vas a descomponer esta sqrt(((175*w^2-15*w^3)/(-100*w^2-169))^2+((150*w^2)/(-100*w^2-169))^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
       _______________________________________
      /                 2                   2 
     /  /     2       3\    /         2    \  
    /   |175*w  - 15*w |    |    150*w     |  
   /    |--------------|  + |--------------|  
  /     |       2      |    |       2      |  
\/      \- 100*w  - 169/    \- 100*w  - 169/  
$$\sqrt{\left(\frac{150 w^{2}}{- 100 w^{2} - 169}\right)^{2} + \left(\frac{- 15 w^{3} + 175 w^{2}}{- 100 w^{2} - 169}\right)^{2}}$$
sqrt(((175*w^2 - 15*w^3)/(-100*w^2 - 169))^2 + ((150*w^2)/(-100*w^2 - 169))^2)
Descomposición de una fracción [src]
sqrt(-5250*w^5/(28561 + 10000*w^4 + 33800*w^2) + 225*w^6/(28561 + 10000*w^4 + 33800*w^2) + 53125*w^4/(28561 + 10000*w^4 + 33800*w^2))
$$\sqrt{\frac{225 w^{6}}{10000 w^{4} + 33800 w^{2} + 28561} - \frac{5250 w^{5}}{10000 w^{4} + 33800 w^{2} + 28561} + \frac{53125 w^{4}}{10000 w^{4} + 33800 w^{2} + 28561}}$$
      ___________________________________________________________________________________________
     /                   5                             6                              4          
    /              5250*w                         225*w                        53125*w           
   /   - --------------------------- + --------------------------- + --------------------------- 
  /                     4          2                  4          2                  4          2 
\/       28561 + 10000*w  + 33800*w    28561 + 10000*w  + 33800*w    28561 + 10000*w  + 33800*w  
Simplificación general [src]
         _________________________
        /  4 /                 2\ 
       /  w *\900 + (-35 + 3*w) / 
5*    /   ----------------------- 
     /                      2     
    /         /           2\      
  \/          \169 + 100*w /      
$$5 \sqrt{\frac{w^{4} \left(\left(3 w - 35\right)^{2} + 900\right)}{\left(100 w^{2} + 169\right)^{2}}}$$
5*sqrt(w^4*(900 + (-35 + 3*w)^2)/(169 + 100*w^2)^2)
Respuesta numérica [src]
1.03550295857988*((w^2 - 0.0857142857142857*w^3)^2/(-1 - 0.591715976331361*w^2)^2 + 0.73469387755102*w^4/(-1 - 0.591715976331361*w^2)^2)^0.5
1.03550295857988*((w^2 - 0.0857142857142857*w^3)^2/(-1 - 0.591715976331361*w^2)^2 + 0.73469387755102*w^4/(-1 - 0.591715976331361*w^2)^2)^0.5
Compilar la expresión [src]
        ________________________________________
       /                   2                    
      /  /      3        2\               4     
     /   \- 15*w  + 175*w /        22500*w      
    /    ------------------- + ---------------- 
   /                      2                   2 
  /        /            2\     /            2\  
\/         \-169 - 100*w /     \-169 - 100*w /  
$$\sqrt{\frac{22500 w^{4}}{\left(- 100 w^{2} - 169\right)^{2}} + \frac{\left(- 15 w^{3} + 175 w^{2}\right)^{2}}{\left(- 100 w^{2} - 169\right)^{2}}}$$
sqrt((-15*w^3 + 175*w^2)^2/(-169 - 100*w^2)^2 + 22500*w^4/(-169 - 100*w^2)^2)
Parte trigonométrica [src]
        ________________________________________
       /                   2                    
      /  /      3        2\               4     
     /   \- 15*w  + 175*w /        22500*w      
    /    ------------------- + ---------------- 
   /                      2                   2 
  /        /            2\     /            2\  
\/         \-169 - 100*w /     \-169 - 100*w /  
$$\sqrt{\frac{22500 w^{4}}{\left(- 100 w^{2} - 169\right)^{2}} + \frac{\left(- 15 w^{3} + 175 w^{2}\right)^{2}}{\left(- 100 w^{2} - 169\right)^{2}}}$$
sqrt((-15*w^3 + 175*w^2)^2/(-169 - 100*w^2)^2 + 22500*w^4/(-169 - 100*w^2)^2)
Abrimos la expresión [src]
        _______________________________________
       /                 2                     
      /  /     2       3\                4     
     /   \175*w  - 15*w /         22500*w      
    /    ----------------- + ----------------- 
   /                     2                   2 
  /      /       2      \    /       2      \  
\/       \- 100*w  - 169/    \- 100*w  - 169/  
$$\sqrt{\frac{22500 w^{4}}{\left(- 100 w^{2} - 169\right)^{2}} + \frac{\left(- 15 w^{3} + 175 w^{2}\right)^{2}}{\left(- 100 w^{2} - 169\right)^{2}}}$$
sqrt((175*w^2 - 15*w^3)^2/(-100*w^2 - 169)^2 + (22500*w^4)/(-100*w^2 - 169)^2)
Denominador común [src]
        ___________________________________________________________________________________________
       /                   5                            6                              4           
      /               210*w                          9*w                         2125*w            
5*   /   - --------------------------- + --------------------------- + --------------------------- 
    /                     4          2                  4          2                  4          2 
  \/       28561 + 10000*w  + 33800*w    28561 + 10000*w  + 33800*w    28561 + 10000*w  + 33800*w  
$$5 \sqrt{\frac{9 w^{6}}{10000 w^{4} + 33800 w^{2} + 28561} - \frac{210 w^{5}}{10000 w^{4} + 33800 w^{2} + 28561} + \frac{2125 w^{4}}{10000 w^{4} + 33800 w^{2} + 28561}}$$
5*sqrt(-210*w^5/(28561 + 10000*w^4 + 33800*w^2) + 9*w^6/(28561 + 10000*w^4 + 33800*w^2) + 2125*w^4/(28561 + 10000*w^4 + 33800*w^2))
Unión de expresiones racionales [src]
         ________________________
        /  4 /                2\ 
       /  w *\900 + (35 - 3*w) / 
5*    /   ---------------------- 
     /                      2    
    /        /            2\     
  \/         \-169 - 100*w /     
$$5 \sqrt{\frac{w^{4} \left(\left(35 - 3 w\right)^{2} + 900\right)}{\left(- 100 w^{2} - 169\right)^{2}}}$$
5*sqrt(w^4*(900 + (35 - 3*w)^2)/(-169 - 100*w^2)^2)
Potencias [src]
        ________________________________________
       /                   2                    
      /  /      3        2\               4     
     /   \- 15*w  + 175*w /        22500*w      
    /    ------------------- + ---------------- 
   /                      2                   2 
  /        /            2\     /            2\  
\/         \-169 - 100*w /     \-169 - 100*w /  
$$\sqrt{\frac{22500 w^{4}}{\left(- 100 w^{2} - 169\right)^{2}} + \frac{\left(- 15 w^{3} + 175 w^{2}\right)^{2}}{\left(- 100 w^{2} - 169\right)^{2}}}$$
sqrt((-15*w^3 + 175*w^2)^2/(-169 - 100*w^2)^2 + 22500*w^4/(-169 - 100*w^2)^2)
Combinatoria [src]
        _____________________________
       /    4 /                  2\  
      /    w *\2125 - 210*w + 9*w /  
5*   /   --------------------------- 
    /                   4          2 
  \/     28561 + 10000*w  + 33800*w  
$$5 \sqrt{\frac{w^{4} \left(9 w^{2} - 210 w + 2125\right)}{10000 w^{4} + 33800 w^{2} + 28561}}$$
5*sqrt(w^4*(2125 - 210*w + 9*w^2)/(28561 + 10000*w^4 + 33800*w^2))
Denominador racional [src]
          ____________________________
         /                 2          
        /  /      2      3\         4 
       /   \- 35*w  + 3*w /  + 900*w  
5*    /    -------------------------- 
     /                        2       
    /           /           2\        
  \/            \169 + 100*w /        
$$5 \sqrt{\frac{900 w^{4} + \left(3 w^{3} - 35 w^{2}\right)^{2}}{\left(100 w^{2} + 169\right)^{2}}}$$
5*sqrt(((-35*w^2 + 3*w^3)^2 + 900*w^4)/(169 + 100*w^2)^2)