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¿Cómo vas a descomponer esta sqrt(((r*r*(r*r+x*x))/((r*r+x*x)^2+(3*r*x)^2))^2+((3*r*r*r*x)/((r*r+x*x)^2+(3*r*x)^2))^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
      _________________________________________________________
     /                          2                            2 
    /  /    r*r*(r*r + x*x)    \    /       3*r*r*r*x       \  
   /   |-----------------------|  + |-----------------------|  
  /    |           2          2|    |           2          2|  
\/     \(r*r + x*x)  + (3*r*x) /    \(r*r + x*x)  + (3*r*x) /  
$$\sqrt{\left(\frac{x r r 3 r}{\left(3 r x\right)^{2} + \left(r r + x x\right)^{2}}\right)^{2} + \left(\frac{r r \left(r r + x x\right)}{\left(3 r x\right)^{2} + \left(r r + x x\right)^{2}}\right)^{2}}$$
sqrt((((r*r)*(r*r + x*x))/((r*r + x*x)^2 + ((3*r)*x)^2))^2 + (((((3*r)*r)*r)*x)/((r*r + x*x)^2 + ((3*r)*x)^2))^2)
Descomposición de una fracción [src]
sqrt(r^8/(r^8 + x^8 + 22*r^2*x^6 + 22*r^6*x^2 + 123*r^4*x^4) + r^4*x^4/(r^8 + x^8 + 22*r^2*x^6 + 22*r^6*x^2 + 123*r^4*x^4) + 11*r^6*x^2/(r^8 + x^8 + 22*r^2*x^6 + 22*r^6*x^2 + 123*r^4*x^4))
$$\sqrt{\frac{r^{8}}{r^{8} + 22 r^{6} x^{2} + 123 r^{4} x^{4} + 22 r^{2} x^{6} + x^{8}} + \frac{11 r^{6} x^{2}}{r^{8} + 22 r^{6} x^{2} + 123 r^{4} x^{4} + 22 r^{2} x^{6} + x^{8}} + \frac{r^{4} x^{4}}{r^{8} + 22 r^{6} x^{2} + 123 r^{4} x^{4} + 22 r^{2} x^{6} + x^{8}}}$$
      ___________________________________________________________________________________________________________________________________
     /                      8                                         4  4                                          6  2                 
    /                      r                                         r *x                                       11*r *x                  
   /   ----------------------------------------- + ----------------------------------------- + ----------------------------------------- 
  /     8    8       2  6       6  2        4  4    8    8       2  6       6  2        4  4    8    8       2  6       6  2        4  4 
\/     r  + x  + 22*r *x  + 22*r *x  + 123*r *x    r  + x  + 22*r *x  + 22*r *x  + 123*r *x    r  + x  + 22*r *x  + 22*r *x  + 123*r *x  
Simplificación general [src]
      ____________________
     /          4         
    /          r          
   /   ------------------ 
  /     4    4       2  2 
\/     r  + x  + 11*r *x  
$$\sqrt{\frac{r^{4}}{r^{4} + 11 r^{2} x^{2} + x^{4}}}$$
sqrt(r^4/(r^4 + x^4 + 11*r^2*x^2))
Respuesta numérica [src]
0.333333333333333*(r^6*x^2/(0.111111111111111*(r^2 + x^2)^2 + r^2*x^2)^2 + 0.111111111111111*r^4*(r^2 + x^2)^2/(0.111111111111111*(r^2 + x^2)^2 + r^2*x^2)^2)^0.5
0.333333333333333*(r^6*x^2/(0.111111111111111*(r^2 + x^2)^2 + r^2*x^2)^2 + 0.111111111111111*r^4*(r^2 + x^2)^2/(0.111111111111111*(r^2 + x^2)^2 + r^2*x^2)^2)^0.5
Denominador común [src]
      ____________________
     /          4         
    /          r          
   /   ------------------ 
  /     4    4       2  2 
\/     r  + x  + 11*r *x  
$$\sqrt{\frac{r^{4}}{r^{4} + 11 r^{2} x^{2} + x^{4}}}$$
sqrt(r^4/(r^4 + x^4 + 11*r^2*x^2))
Parte trigonométrica [src]
         ___________________________________________________
        /                  2                                
       /        4 / 2    2\                    6  2         
      /        r *\r  + x /                 9*r *x          
     /    ----------------------- + ----------------------- 
    /                           2                         2 
   /      /         2          \    /         2          \  
  /       |/ 2    2\       2  2|    |/ 2    2\       2  2|  
\/        \\r  + x /  + 9*r *x /    \\r  + x /  + 9*r *x /  
$$\sqrt{\frac{9 r^{6} x^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}} + \frac{r^{4} \left(r^{2} + x^{2}\right)^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}}}$$
sqrt(r^4*(r^2 + x^2)^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2 + 9*r^6*x^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2)
Compilar la expresión [src]
         ___________________________________________________
        /                  2                                
       /        4 / 2    2\                    6  2         
      /        r *\r  + x /                 9*r *x          
     /    ----------------------- + ----------------------- 
    /                           2                         2 
   /      /         2          \    /         2          \  
  /       |/ 2    2\       2  2|    |/ 2    2\       2  2|  
\/        \\r  + x /  + 9*r *x /    \\r  + x /  + 9*r *x /  
$$\sqrt{\frac{9 r^{6} x^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}} + \frac{r^{4} \left(r^{2} + x^{2}\right)^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}}}$$
sqrt(r^4*(r^2 + x^2)^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2 + 9*r^6*x^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2)
Combinatoria [src]
      ____________________
     /          4         
    /          r          
   /   ------------------ 
  /     4    4       2  2 
\/     r  + x  + 11*r *x  
$$\sqrt{\frac{r^{4}}{r^{4} + 11 r^{2} x^{2} + x^{4}}}$$
sqrt(r^4/(r^4 + x^4 + 11*r^2*x^2))
Denominador racional [src]
        _________________________________
       /       /         2          \    
      /      4 |/ 2    2\       2  2|    
     /      r *\\r  + x /  + 9*r *x /    
    /    ------------------------------- 
   /                                   2 
  /      / 4    4          2      2  2\  
\/       \r  + x  + (3*r*x)  + 2*r *x /  
$$\sqrt{\frac{r^{4} \left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)}{\left(r^{4} + 2 r^{2} x^{2} + x^{4} + \left(3 r x\right)^{2}\right)^{2}}}$$
sqrt(r^4*((r^2 + x^2)^2 + 9*r^2*x^2)/(r^4 + x^4 + ((3*r)*x)^2 + 2*r^2*x^2)^2)
Abrimos la expresión [src]
       _______________________________________________________
      /       4            2                    6  2          
     /       r *(r*r + x*x)                  9*r *x           
    /   ------------------------- + ------------------------- 
   /                            2                           2 
  /     /           2    2    2\    /           2    2    2\  
\/      \(r*r + x*x)  + x *9*r /    \(r*r + x*x)  + x *9*r /  
$$\sqrt{\frac{9 r^{6} x^{2}}{\left(9 r^{2} x^{2} + \left(r r + x x\right)^{2}\right)^{2}} + \frac{r^{4} \left(r r + x x\right)^{2}}{\left(9 r^{2} x^{2} + \left(r r + x x\right)^{2}\right)^{2}}}$$
sqrt(r^4*(r*r + x*x)^2/((r*r + x*x)^2 + x^2*(9*r^2))^2 + 9*r^6*x^2/((r*r + x*x)^2 + x^2*(9*r^2))^2)
Potencias [src]
         ___________________________________________________
        /                  2                                
       /        4 / 2    2\                    6  2         
      /        r *\r  + x /                 9*r *x          
     /    ----------------------- + ----------------------- 
    /                           2                         2 
   /      /         2          \    /         2          \  
  /       |/ 2    2\       2  2|    |/ 2    2\       2  2|  
\/        \\r  + x /  + 9*r *x /    \\r  + x /  + 9*r *x /  
$$\sqrt{\frac{9 r^{6} x^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}} + \frac{r^{4} \left(r^{2} + x^{2}\right)^{2}}{\left(9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}\right)^{2}}}$$
sqrt(r^4*(r^2 + x^2)^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2 + 9*r^6*x^2/((r^2 + x^2)^2 + 9*r^2*x^2)^2)
Unión de expresiones racionales [src]
       ______________________
      /           4          
     /           r           
    /   -------------------- 
   /             2           
  /     / 2    2\       2  2 
\/      \r  + x /  + 9*r *x  
$$\sqrt{\frac{r^{4}}{9 r^{2} x^{2} + \left(r^{2} + x^{2}\right)^{2}}}$$
sqrt(r^4/((r^2 + x^2)^2 + 9*r^2*x^2))