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Simplificación de expresiones/ Descomposición en fracciones simples/ (w*(((t2+t3)^2*w^2)+(t2*t3*w^2+k2*k3-1)^2))/((t2*t3*w^2+k2*k3-1)*w*k2*k3)

¿Cómo vas a descomponer esta (w*(((t2+t3)^2*w^2)+(t2*t3*w^2+k2*k3-1)^2))/((t2*t3*w^2+k2*k3-1)*w*k2*k3) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  /                                      2\
  |         2  2   /       2            \ |
w*\(t2 + t3) *w  + \t2*t3*w  + k2*k3 - 1/ /
-------------------------------------------
       /       2            \              
       \t2*t3*w  + k2*k3 - 1/*w*k2*k3
$$\frac{w \left(w^{2} \left(t_{2} + t_{3}\right)^{2} + \left(\left(k_{2} k_{3} + w^{2} t_{2} t_{3}\right) - 1\right)^{2}\right)}{k_{3} k_{2} w \left(\left(k_{2} k_{3} + w^{2} t_{2} t_{3}\right) - 1\right)}$$ 
(w*((t2 + t3)^2*w^2 + ((t2*t3)*w^2 + k2*k3 - 1)^2))/((((((t2*t3)*w^2 + k2*k3 - 1)*w)*k2)*k3))
Simplificación general [src] 
                       2                
/                    2\     2          2
\-1 + k2*k3 + t2*t3*w /  + w *(t2 + t3) 
----------------------------------------
           /                    2\      
     k2*k3*\-1 + k2*k3 + t2*t3*w /
$$\frac{w^{2} \left(t_{2} + t_{3}\right)^{2} + \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)^{2}}{k_{2} k_{3} \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)}$$ 
((-1 + k2*k3 + t2*t3*w^2)^2 + w^2*(t2 + t3)^2)/(k2*k3*(-1 + k2*k3 + t2*t3*w^2))
Respuesta numérica [src] 
((-1.0 + k2*k3 + t2*t3*w^2)^2 + w^2*(t2 + t3)^2)/(k2*k3*(-1.0 + k2*k3 + t2*t3*w^2))
((-1.0 + k2*k3 + t2*t3*w^2)^2 + w^2*(t2 + t3)^2)/(k2*k3*(-1.0 + k2*k3 + t2*t3*w^2))
Parte trigonométrica [src] 
                       2                
/                    2\     2          2
\-1 + k2*k3 + t2*t3*w /  + w *(t2 + t3) 
----------------------------------------
           /                    2\      
     k2*k3*\-1 + k2*k3 + t2*t3*w /
$$\frac{w^{2} \left(t_{2} + t_{3}\right)^{2} + \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)^{2}}{k_{2} k_{3} \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)}$$ 
((-1 + k2*k3 + t2*t3*w^2)^2 + w^2*(t2 + t3)^2)/(k2*k3*(-1 + k2*k3 + t2*t3*w^2))
Denominador racional [src] 
                       2                
/                    2\     2          2
\-1 + k2*k3 + t2*t3*w /  + w *(t2 + t3) 
----------------------------------------
           /                    2\      
     k2*k3*\-1 + k2*k3 + t2*t3*w /
$$\frac{w^{2} \left(t_{2} + t_{3}\right)^{2} + \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)^{2}}{k_{2} k_{3} \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)}$$ 
((-1 + k2*k3 + t2*t3*w^2)^2 + w^2*(t2 + t3)^2)/(k2*k3*(-1 + k2*k3 + t2*t3*w^2))
Unión de expresiones racionales [src] 
                       2                
/                    2\     2          2
\-1 + k2*k3 + t2*t3*w /  + w *(t2 + t3) 
----------------------------------------
           /                    2\      
     k2*k3*\-1 + k2*k3 + t2*t3*w /
$$\frac{w^{2} \left(t_{2} + t_{3}\right)^{2} + \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)^{2}}{k_{2} k_{3} \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)}$$ 
((-1 + k2*k3 + t2*t3*w^2)^2 + w^2*(t2 + t3)^2)/(k2*k3*(-1 + k2*k3 + t2*t3*w^2))
Denominador común [src] 
          2  2     2  2     2   2     2   2  4
    1 + t2 *w  + t3 *w  - k2 *k3  + t2 *t3 *w 
2 + ------------------------------------------
           2   2                        2     
         k2 *k3  - k2*k3 + k2*k3*t2*t3*w
$$2 + \frac{- k_{2}^{2} k_{3}^{2} + t_{2}^{2} t_{3}^{2} w^{4} + t_{2}^{2} w^{2} + t_{3}^{2} w^{2} + 1}{k_{2}^{2} k_{3}^{2} + k_{2} k_{3} t_{2} t_{3} w^{2} - k_{2} k_{3}}$$ 
2 + (1 + t2^2*w^2 + t3^2*w^2 - k2^2*k3^2 + t2^2*t3^2*w^4)/(k2^2*k3^2 - k2*k3 + k2*k3*t2*t3*w^2)
Abrimos la expresión [src] 
                                      2
         2  2   /       2            \ 
(t2 + t3) *w  + \t2*t3*w  + k2*k3 - 1/ 
---------------------------------------
            /       2            \     
      k2*k3*\t2*t3*w  + k2*k3 - 1/
$$\frac{w^{2} \left(t_{2} + t_{3}\right)^{2} + \left(\left(k_{2} k_{3} + w^{2} t_{2} t_{3}\right) - 1\right)^{2}}{k_{2} k_{3} \left(\left(k_{2} k_{3} + w^{2} t_{2} t_{3}\right) - 1\right)}$$ 
((t2 + t3)^2*w^2 + ((t2*t3)*w^2 + k2*k3 - 1)^2)/(k2*k3*((t2*t3)*w^2 + k2*k3 - 1))
Potencias [src] 
                       2                
/                    2\     2          2
\-1 + k2*k3 + t2*t3*w /  + w *(t2 + t3) 
----------------------------------------
           /                    2\      
     k2*k3*\-1 + k2*k3 + t2*t3*w /
$$\frac{w^{2} \left(t_{2} + t_{3}\right)^{2} + \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)^{2}}{k_{2} k_{3} \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)}$$ 
((-1 + k2*k3 + t2*t3*w^2)^2 + w^2*(t2 + t3)^2)/(k2*k3*(-1 + k2*k3 + t2*t3*w^2))
Compilar la expresión [src] 
                       2                
/                    2\     2          2
\-1 + k2*k3 + t2*t3*w /  + w *(t2 + t3) 
----------------------------------------
           /                    2\      
     k2*k3*\-1 + k2*k3 + t2*t3*w /
$$\frac{w^{2} \left(t_{2} + t_{3}\right)^{2} + \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)^{2}}{k_{2} k_{3} \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)}$$ 
((-1 + k2*k3 + t2*t3*w^2)^2 + w^2*(t2 + t3)^2)/(k2*k3*(-1 + k2*k3 + t2*t3*w^2))
Combinatoria [src] 
      2   2     2  2     2  2               2   2  4                  2
1 + k2 *k3  + t2 *w  + t3 *w  - 2*k2*k3 + t2 *t3 *w  + 2*k2*k3*t2*t3*w 
-----------------------------------------------------------------------
                           /                    2\                     
                     k2*k3*\-1 + k2*k3 + t2*t3*w /
$$\frac{k_{2}^{2} k_{3}^{2} + 2 k_{2} k_{3} t_{2} t_{3} w^{2} - 2 k_{2} k_{3} + t_{2}^{2} t_{3}^{2} w^{4} + t_{2}^{2} w^{2} + t_{3}^{2} w^{2} + 1}{k_{2} k_{3} \left(k_{2} k_{3} + t_{2} t_{3} w^{2} - 1\right)}$$ 
(1 + k2^2*k3^2 + t2^2*w^2 + t3^2*w^2 - 2*k2*k3 + t2^2*t3^2*w^4 + 2*k2*k3*t2*t3*w^2)/(k2*k3*(-1 + k2*k3 + t2*t3*w^2))
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