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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
      __________________________
     /   2 /  2\              2 
    /   w *\-t /   /   t*w   \  
   /   --------- + |---------|  
  /         2  2   |     2  2|  
\/     1 + t *w    \1 + t *w /
−t2w2t2w2+1+(twt2w2+1)2\sqrt{\frac{- t^{2} w^{2}}{t^{2} w^{2} + 1} + \left(\frac{t w}{t^{2} w^{2} + 1}\right)^{2}} 
sqrt((w^2*(-t^2))/(1 + t^2*w^2) + ((t*w)/(1 + t^2*w^2))^2)
Descomposición de una fracción [src] 
sqrt((w^2*(-t^2))/(1 + t^2*w^2) + t^2*w^2/(1 + t^4*w^4 + 2*t^2*w^2))
t2w2t4w4+2t2w2+1+−t2w2t2w2+1\sqrt{\frac{t^{2} w^{2}}{t^{4} w^{4} + 2 t^{2} w^{2} + 1} + \frac{- t^{2} w^{2}}{t^{2} w^{2} + 1}} 
      _________________________________
     /   2 /  2\           2  2        
    /   w *\-t /          t *w         
   /   --------- + ------------------- 
  /         2  2        4  4      2  2 
\/     1 + t *w    1 + t *w  + 2*t *w
Simplificación general [src] 
       ______________
      /     4  4     
     /    -t *w      
    /   ------------ 
   /               2 
  /     /     2  2\  
\/      \1 + t *w /
−t4w4(t2w2+1)2\sqrt{- \frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}}} 
sqrt(-t^4*w^4/(1 + t^2*w^2)^2)
Respuesta numérica [src] 
(t^2*w^2/(1.0 + t^2*w^2)^2 - t^2*w^2/(1.0 + t^2*w^2))^0.5
(t^2*w^2/(1.0 + t^2*w^2)^2 - t^2*w^2/(1.0 + t^2*w^2))^0.5
Denominador común [src] 
      _________________________________
     /         2  2             2  2   
    /         t *w             t *w    
   /   ------------------- - --------- 
  /         4  4      2  2        2  2 
\/     1 + t *w  + 2*t *w    1 + t *w
t2w2t4w4+2t2w2+1−t2w2t2w2+1\sqrt{\frac{t^{2} w^{2}}{t^{4} w^{4} + 2 t^{2} w^{2} + 1} - \frac{t^{2} w^{2}}{t^{2} w^{2} + 1}} 
sqrt(t^2*w^2/(1 + t^4*w^4 + 2*t^2*w^2) - t^2*w^2/(1 + t^2*w^2))
Combinatoria [src] 
      _____________________
     /         4  4        
    /        -t *w         
   /   ------------------- 
  /         4  4      2  2 
\/     1 + t *w  + 2*t *w
−t4w4t4w4+2t2w2+1\sqrt{- \frac{t^{4} w^{4}}{t^{4} w^{4} + 2 t^{2} w^{2} + 1}} 
sqrt(-t^4*w^4/(1 + t^4*w^4 + 2*t^2*w^2))
Abrimos la expresión [src] 
       __________________________
      /     2  2         2 /  2\ 
     /     t *w         w *\-t / 
    /   ------------ + --------- 
   /               2        2  2 
  /     /     2  2\    1 + t *w  
\/      \1 + t *w /
t2w2(t2w2+1)2+−t2w2t2w2+1\sqrt{\frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{- t^{2} w^{2}}{t^{2} w^{2} + 1}} 
sqrt((t^2*w^2)/(1 + t^2*w^2)^2 + (w^2*(-t^2))/(1 + t^2*w^2))
Compilar la expresión [src] 
       _______________________________
      /    /      2             2   \ 
     /   2 |     t             t    | 
    /   w *|------------ - ---------| 
   /       |           2        2  2| 
  /        |/     2  2\    1 + t *w | 
\/         \\1 + t *w /             /
w2(−t2t2w2+1+t2(t2w2+1)2)\sqrt{w^{2} \left(- \frac{t^{2}}{t^{2} w^{2} + 1} + \frac{t^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}\right)} 
       _______________________________
      /    /      2             2   \ 
     /   2 |     w             w    | 
    /   t *|------------ - ---------| 
   /       |           2        2  2| 
  /        |/     2  2\    1 + t *w | 
\/         \\1 + t *w /             /
t2(−w2t2w2+1+w2(t2w2+1)2)\sqrt{t^{2} \left(- \frac{w^{2}}{t^{2} w^{2} + 1} + \frac{w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}\right)} 
       __________________________
      /     2  2          2  2   
     /     t *w          t *w    
    /   ------------ - --------- 
   /               2        2  2 
  /     /     2  2\    1 + t *w  
\/      \1 + t *w /
−t2w2t2w2+1+t2w2(t2w2+1)2\sqrt{- \frac{t^{2} w^{2}}{t^{2} w^{2} + 1} + \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^2*w^2/(1 + t^2*w^2))
Denominador racional [src] 
       ______________
      /     4  4     
     /    -t *w      
    /   ------------ 
   /               2 
  /     /     2  2\  
\/      \1 + t *w /
−t4w4(t2w2+1)2\sqrt{- \frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}}} 
sqrt(-t^4*w^4/(1 + t^2*w^2)^2)
Unión de expresiones racionales [src] 
       ______________
      /     4  4     
     /    -t *w      
    /   ------------ 
   /               2 
  /     /     2  2\  
\/      \1 + t *w /
−t4w4(t2w2+1)2\sqrt{- \frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}}} 
sqrt(-t^4*w^4/(1 + t^2*w^2)^2)
Potencias [src] 
       __________________________
      /     2  2          2  2   
     /     t *w          t *w    
    /   ------------ - --------- 
   /               2        2  2 
  /     /     2  2\    1 + t *w  
\/      \1 + t *w /
−t2w2t2w2+1+t2w2(t2w2+1)2\sqrt{- \frac{t^{2} w^{2}}{t^{2} w^{2} + 1} + \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^2*w^2/(1 + t^2*w^2))
Parte trigonométrica [src] 
       __________________________
      /     2  2          2  2   
     /     t *w          t *w    
    /   ------------ - --------- 
   /               2        2  2 
  /     /     2  2\    1 + t *w  
\/      \1 + t *w /
−t2w2t2w2+1+t2w2(t2w2+1)2\sqrt{- \frac{t^{2} w^{2}}{t^{2} w^{2} + 1} + \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^2*w^2/(1 + t^2*w^2))
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