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¿Cómo vas a descomponer esta sqrt((-9*w/(w^4-79*w^2+1))^2+(-9*w/(w^4-79*w^2+1))^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
      _______________________________________
     /                 2                   2 
    /  /     -9*w     \    /     -9*w     \  
   /   |--------------|  + |--------------|  
  /    | 4       2    |    | 4       2    |  
\/     \w  - 79*w  + 1/    \w  - 79*w  + 1/  
$$\sqrt{\left(\frac{\left(-1\right) 9 w}{\left(w^{4} - 79 w^{2}\right) + 1}\right)^{2} + \left(\frac{\left(-1\right) 9 w}{\left(w^{4} - 79 w^{2}\right) + 1}\right)^{2}}$$
sqrt(((-9*w)/(w^4 - 79*w^2 + 1))^2 + ((-9*w)/(w^4 - 79*w^2 + 1))^2)
Descomposición de una fracción [src]
9*sqrt(2)*sqrt(w^2/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4))
$$9 \sqrt{2} \sqrt{\frac{w^{2}}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1}}$$
              ____________________________________
             /                  2                 
    ___     /                  w                  
9*\/ 2 *   /   ---------------------------------- 
          /         8        2        6         4 
        \/     1 + w  - 158*w  - 158*w  + 6243*w  
Simplificación general [src]
               ___________________
              /          2        
    ___      /          w         
9*\/ 2 *    /   ----------------- 
           /                    2 
          /     /     4       2\  
        \/      \1 + w  - 79*w /  
$$9 \sqrt{2} \sqrt{\frac{w^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}}}$$
9*sqrt(2)*sqrt(w^2/(1 + w^4 - 79*w^2)^2)
Respuesta numérica [src]
0.161112937485542*(w^2/(0.0126582278481013 - w^2 + 0.0126582278481013*w^4)^2)^0.5
0.161112937485542*(w^2/(0.0126582278481013 - w^2 + 0.0126582278481013*w^4)^2)^0.5
Denominador racional [src]
               ___________________
              /          2        
    ___      /          w         
9*\/ 2 *    /   ----------------- 
           /                    2 
          /     /     4       2\  
        \/      \1 + w  - 79*w /  
$$9 \sqrt{2} \sqrt{\frac{w^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}}}$$
9*sqrt(2)*sqrt(w^2/(1 + w^4 - 79*w^2)^2)
Compilar la expresión [src]
               ___________________
              /          2        
    ___      /          w         
9*\/ 2 *    /   ----------------- 
           /                    2 
          /     /     4       2\  
        \/      \1 + w  - 79*w /  
$$9 \sqrt{2} \sqrt{\frac{w^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}}}$$
9*sqrt(2)*sqrt(w^2/(1 + w^4 - 79*w^2)^2)
Combinatoria [src]
              ____________________________________
             /                  2                 
    ___     /                  w                  
9*\/ 2 *   /   ---------------------------------- 
          /         8        2        6         4 
        \/     1 + w  - 158*w  - 158*w  + 6243*w  
$$9 \sqrt{2} \sqrt{\frac{w^{2}}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1}}$$
9*sqrt(2)*sqrt(w^2/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4))
Parte trigonométrica [src]
               ___________________
              /          2        
    ___      /          w         
9*\/ 2 *    /   ----------------- 
           /                    2 
          /     /     4       2\  
        \/      \1 + w  - 79*w /  
$$9 \sqrt{2} \sqrt{\frac{w^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}}}$$
9*sqrt(2)*sqrt(w^2/(1 + w^4 - 79*w^2)^2)
Potencias [src]
               ___________________
              /          2        
    ___      /          w         
9*\/ 2 *    /   ----------------- 
           /                    2 
          /     /     4       2\  
        \/      \1 + w  - 79*w /  
$$9 \sqrt{2} \sqrt{\frac{w^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}}}$$
9*sqrt(2)*sqrt(w^2/(1 + w^4 - 79*w^2)^2)
Abrimos la expresión [src]
               ___________________
              /          2        
  ___        /          w         
\/ 2 *9*    /   ----------------- 
           /                    2 
          /     / 4       2    \  
        \/      \w  - 79*w  + 1/  
$$\sqrt{2} \cdot 9 \sqrt{\frac{w^{2}}{\left(\left(w^{4} - 79 w^{2}\right) + 1\right)^{2}}}$$
sqrt(2)*(9*sqrt(w^2/(w^4 - 79*w^2 + 1)^2))
Unión de expresiones racionales [src]
               ______________________
              /           2          
    ___      /           w           
9*\/ 2 *    /   -------------------- 
           /                       2 
          /     /     2 /       2\\  
        \/      \1 + w *\-79 + w //  
$$9 \sqrt{2} \sqrt{\frac{w^{2}}{\left(w^{2} \left(w^{2} - 79\right) + 1\right)^{2}}}$$
9*sqrt(2)*sqrt(w^2/(1 + w^2*(-79 + w^2))^2)
Denominador común [src]
              ____________________________________
             /                  2                 
    ___     /                  w                  
9*\/ 2 *   /   ---------------------------------- 
          /         8        2        6         4 
        \/     1 + w  - 158*w  - 158*w  + 6243*w  
$$9 \sqrt{2} \sqrt{\frac{w^{2}}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1}}$$
9*sqrt(2)*sqrt(w^2/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4))