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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt((-9*w/(w^4-79*w^2+1))^2+((w^2+1)/(w^4-79*w^2+1))^2)

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

Expresión a simplificar:

Solución

Ha introducido [src] 
       _______________________________________
      /                                     2 
     /                  2   /     2        \  
    /   /     -9*w     \    |    w  + 1    |  
   /    |--------------|  + |--------------|  
  /     | 4       2    |    | 4       2    |  
\/      \w  - 79*w  + 1/    \w  - 79*w  + 1/
((−1)9w(w4−79w2)+1)2+(w2+1(w4−79w2)+1)2\sqrt{\left(\frac{\left(-1\right) 9 w}{\left(w^{4} - 79 w^{2}\right) + 1}\right)^{2} + \left(\frac{w^{2} + 1}{\left(w^{4} - 79 w^{2}\right) + 1}\right)^{2}} 
sqrt(((-9*w)/(w^4 - 79*w^2 + 1))^2 + ((w^2 + 1)/(w^4 - 79*w^2 + 1))^2)
Descomposición de una fracción [src] 
sqrt(1/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4) + w^4/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4) + 83*w^2/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4))
w4w8−158w6+6243w4−158w2+1+83w2w8−158w6+6243w4−158w2+1+1w8−158w6+6243w4−158w2+1\sqrt{\frac{w^{4}}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1} + \frac{83 w^{2}}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1} + \frac{1}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1}} 
      ______________________________________________________________________________________________________________
     /                                                       4                                     2                
    /                  1                                    w                                  83*w                 
   /   ---------------------------------- + ---------------------------------- + ---------------------------------- 
  /         8        2        6         4        8        2        6         4        8        2        6         4 
\/     1 + w  - 158*w  - 158*w  + 6243*w    1 + w  - 158*w  - 158*w  + 6243*w    1 + w  - 158*w  - 158*w  + 6243*w
Simplificación general [src] 
        ___________________
       /         2         
      /  /     2\        2 
     /   \1 + w /  + 81*w  
    /    ----------------- 
   /                     2 
  /      /     4       2\  
\/       \1 + w  - 79*w /
81w2+(w2+1)2(w4−79w2+1)2\sqrt{\frac{81 w^{2} + \left(w^{2} + 1\right)^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}}} 
sqrt(((1 + w^2)^2 + 81*w^2)/(1 + w^4 - 79*w^2)^2)
Abrimos la expresión [src] 
        _______________________________________
       /             2                         
      /      / 2    \                  2       
     /       \w  + 1/              81*w        
    /    ----------------- + ----------------- 
   /                     2                   2 
  /      / 4       2    \    / 4       2    \  
\/       \w  - 79*w  + 1/    \w  - 79*w  + 1/
81w2((w4−79w2)+1)2+(w2+1)2((w4−79w2)+1)2\sqrt{\frac{81 w^{2}}{\left(\left(w^{4} - 79 w^{2}\right) + 1\right)^{2}} + \frac{\left(w^{2} + 1\right)^{2}}{\left(\left(w^{4} - 79 w^{2}\right) + 1\right)^{2}}} 
sqrt((w^2 + 1)^2/(w^4 - 79*w^2 + 1)^2 + (81*w^2)/(w^4 - 79*w^2 + 1)^2)
Respuesta numérica [src] 
0.113924050632911*(w^2/(0.0126582278481013 - w^2 + 0.0126582278481013*w^4)^2 + 0.0123456790123457*(1.0 + w^2)^2/(0.0126582278481013 - w^2 + 0.0126582278481013*w^4)^2)^0.5
0.113924050632911*(w^2/(0.0126582278481013 - w^2 + 0.0126582278481013*w^4)^2 + 0.0123456790123457*(1.0 + w^2)^2/(0.0126582278481013 - w^2 + 0.0126582278481013*w^4)^2)^0.5
Parte trigonométrica [src] 
        _______________________________________
       /             2                         
      /      /     2\                  2       
     /       \1 + w /              81*w        
    /    ----------------- + ----------------- 
   /                     2                   2 
  /      /     4       2\    /     4       2\  
\/       \1 + w  - 79*w /    \1 + w  - 79*w /
81w2(w4−79w2+1)2+(w2+1)2(w4−79w2+1)2\sqrt{\frac{81 w^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}} + \frac{\left(w^{2} + 1\right)^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}}} 
sqrt((1 + w^2)^2/(1 + w^4 - 79*w^2)^2 + 81*w^2/(1 + w^4 - 79*w^2)^2)
Denominador común [src] 
      ______________________________________________________________________________________________________________
     /                                                       4                                     2                
    /                  1                                    w                                  83*w                 
   /   ---------------------------------- + ---------------------------------- + ---------------------------------- 
  /         8        2        6         4        8        2        6         4        8        2        6         4 
\/     1 + w  - 158*w  - 158*w  + 6243*w    1 + w  - 158*w  - 158*w  + 6243*w    1 + w  - 158*w  - 158*w  + 6243*w
w4w8−158w6+6243w4−158w2+1+83w2w8−158w6+6243w4−158w2+1+1w8−158w6+6243w4−158w2+1\sqrt{\frac{w^{4}}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1} + \frac{83 w^{2}}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1} + \frac{1}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1}} 
sqrt(1/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4) + w^4/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4) + 83*w^2/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4))
Combinatoria [src] 
      ____________________________________
     /                4       2           
    /            1 + w  + 83*w            
   /   ---------------------------------- 
  /         8        2        6         4 
\/     1 + w  - 158*w  - 158*w  + 6243*w
w4+83w2+1w8−158w6+6243w4−158w2+1\sqrt{\frac{w^{4} + 83 w^{2} + 1}{w^{8} - 158 w^{6} + 6243 w^{4} - 158 w^{2} + 1}} 
sqrt((1 + w^4 + 83*w^2)/(1 + w^8 - 158*w^2 - 158*w^6 + 6243*w^4))
Denominador racional [src] 
        ___________________
       /         2         
      /  /     2\        2 
     /   \1 + w /  + 81*w  
    /    ----------------- 
   /                     2 
  /      / 4       2    \  
\/       \w  - 79*w  + 1/
81w2+(w2+1)2((w4−79w2)+1)2\sqrt{\frac{81 w^{2} + \left(w^{2} + 1\right)^{2}}{\left(\left(w^{4} - 79 w^{2}\right) + 1\right)^{2}}} 
sqrt(((1 + w^2)^2 + 81*w^2)/(w^4 - 79*w^2 + 1)^2)
Compilar la expresión [src] 
        _______________________________________
       /             2                         
      /      /     2\                  2       
     /       \1 + w /              81*w        
    /    ----------------- + ----------------- 
   /                     2                   2 
  /      /     4       2\    /     4       2\  
\/       \1 + w  - 79*w /    \1 + w  - 79*w /
81w2(w4−79w2+1)2+(w2+1)2(w4−79w2+1)2\sqrt{\frac{81 w^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}} + \frac{\left(w^{2} + 1\right)^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}}} 
sqrt((1 + w^2)^2/(1 + w^4 - 79*w^2)^2 + 81*w^2/(1 + w^4 - 79*w^2)^2)
Potencias [src] 
        _______________________________________
       /             2                         
      /      /     2\                  2       
     /       \1 + w /              81*w        
    /    ----------------- + ----------------- 
   /                     2                   2 
  /      /     4       2\    /     4       2\  
\/       \1 + w  - 79*w /    \1 + w  - 79*w /
81w2(w4−79w2+1)2+(w2+1)2(w4−79w2+1)2\sqrt{\frac{81 w^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}} + \frac{\left(w^{2} + 1\right)^{2}}{\left(w^{4} - 79 w^{2} + 1\right)^{2}}} 
sqrt((1 + w^2)^2/(1 + w^4 - 79*w^2)^2 + 81*w^2/(1 + w^4 - 79*w^2)^2)
Unión de expresiones racionales [src] 
        ______________________
       /          2           
      /   /     2\        2   
     /    \1 + w /  + 81*w    
    /    -------------------- 
   /                        2 
  /      /     2 /       2\\  
\/       \1 + w *\-79 + w //
81w2+(w2+1)2(w2(w2−79)+1)2\sqrt{\frac{81 w^{2} + \left(w^{2} + 1\right)^{2}}{\left(w^{2} \left(w^{2} - 79\right) + 1\right)^{2}}} 
sqrt(((1 + w^2)^2 + 81*w^2)/(1 + w^2*(-79 + w^2))^2)
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