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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
       _____________________________
      /            2                
     /  /  2 /  2\\               2 
    /   | w *\-t /|    /   t*w   \  
   /    |---------|  + |---------|  
  /     |     2  2|    |     2  2|  
\/      \1 + t *w /    \1 + t *w /
(twt2w2+1)2+(−t2w2t2w2+1)2\sqrt{\left(\frac{t w}{t^{2} w^{2} + 1}\right)^{2} + \left(\frac{- t^{2} w^{2}}{t^{2} w^{2} + 1}\right)^{2}} 
sqrt(((w^2*(-t^2))/(1 + t^2*w^2))^2 + ((t*w)/(1 + t^2*w^2))^2)
Descomposición de una fracción [src] 
sqrt(t^2*w^2/(1 + t^4*w^4 + 2*t^2*w^2) + t^4*w^4/(1 + t^4*w^4 + 2*t^2*w^2))
t4w4t4w4+2t2w2+1+t2w2t4w4+2t2w2+1\sqrt{\frac{t^{4} w^{4}}{t^{4} w^{4} + 2 t^{2} w^{2} + 1} + \frac{t^{2} w^{2}}{t^{4} w^{4} + 2 t^{2} w^{2} + 1}} 
      ___________________________________________
     /         2  2                  4  4        
    /         t *w                  t *w         
   /   ------------------- + ------------------- 
  /         4  4      2  2        4  4      2  2 
\/     1 + t *w  + 2*t *w    1 + t *w  + 2*t *w
Simplificación general [src] 
      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w
t2w2t2w2+1\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}} 
sqrt(t^2*w^2/(1 + t^2*w^2))
Respuesta numérica [src] 
(t^2*w^2/(1.0 + t^2*w^2)^2 + t^4*w^4/(1.0 + t^2*w^2)^2)^0.5
(t^2*w^2/(1.0 + t^2*w^2)^2 + t^4*w^4/(1.0 + t^2*w^2)^2)^0.5
Parte trigonométrica [src] 
       _____________________________
      /     2  2           4  4     
     /     t *w           t *w      
    /   ------------ + ------------ 
   /               2              2 
  /     /     2  2\    /     2  2\  
\/      \1 + t *w /    \1 + t *w /
t4w4(t2w2+1)2+t2w2(t2w2+1)2\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}} 
sqrt(t^2*w^2/(1 + t^2*w^2)^2 + t^4*w^4/(1 + t^2*w^2)^2)
Potencias [src] 
       _____________________________
      /     2  2           4  4     
     /     t *w           t *w      
    /   ------------ + ------------ 
   /               2              2 
  /     /     2  2\    /     2  2\  
\/      \1 + t *w /    \1 + t *w /
t4w4(t2w2+1)2+t2w2(t2w2+1)2\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}} 
sqrt(t^2*w^2/(1 + t^2*w^2)^2 + t^4*w^4/(1 + t^2*w^2)^2)
Combinatoria [src] 
      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w
t2w2t2w2+1\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}} 
sqrt(t^2*w^2/(1 + t^2*w^2))
Unión de expresiones racionales [src] 
      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w
t2w2t2w2+1\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}} 
sqrt(t^2*w^2/(1 + t^2*w^2))
Compilar la expresión [src] 
       _____________________________
      /     2  2           4  4     
     /     t *w           t *w      
    /   ------------ + ------------ 
   /               2              2 
  /     /     2  2\    /     2  2\  
\/      \1 + t *w /    \1 + t *w /
t4w4(t2w2+1)2+t2w2(t2w2+1)2\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}} 
sqrt(t^2*w^2/(1 + t^2*w^2)^2 + t^4*w^4/(1 + t^2*w^2)^2)
Denominador racional [src] 
      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w
t2w2t2w2+1\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}} 
sqrt(t^2*w^2/(1 + t^2*w^2))
Abrimos la expresión [src] 
       _____________________________
      /     2  2           4  4     
     /     t *w           t *w      
    /   ------------ + ------------ 
   /               2              2 
  /     /     2  2\    /     2  2\  
\/      \1 + t *w /    \1 + t *w /
t4w4(t2w2+1)2+t2w2(t2w2+1)2\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}} 
sqrt((t^2*w^2)/(1 + t^2*w^2)^2 + (t^4*w^4)/(1 + t^2*w^2)^2)
Denominador común [src] 
      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w
t2w2t2w2+1\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}} 
sqrt(t^2*w^2/(1 + t^2*w^2))
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