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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(x)/(1-x^2/pi^2)

¿Cómo vas a descomponer esta sin(x)/(1-x^2/pi^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
 sin(x)
-------
      2
     x 
1 - ---
      2
    pi
$$\frac{\sin{\left(x \right)}}{- \frac{x^{2}}{\pi^{2}} + 1}$$ 
sin(x)/(1 - x^2/pi^2)
Simplificación general [src] 
   2        
-pi *sin(x) 
------------
   2     2  
  x  - pi
$$- \frac{\pi^{2} \sin{\left(x \right)}}{x^{2} - \pi^{2}}$$ 
-pi^2*sin(x)/(x^2 - pi^2)
Respuesta numérica [src] 
sin(x)/(1.0 - 0.101321183642338*x^2)
sin(x)/(1.0 - 0.101321183642338*x^2)
Denominador racional [src] 
  2       
pi *sin(x)
----------
   2    2 
 pi  - x
$$\frac{\pi^{2} \sin{\left(x \right)}}{- x^{2} + \pi^{2}}$$ 
pi^2*sin(x)/(pi^2 - x^2)
Denominador común [src] 
   2        
-pi *sin(x) 
------------
   2     2  
  x  - pi
$$- \frac{\pi^{2} \sin{\left(x \right)}}{x^{2} - \pi^{2}}$$ 
-pi^2*sin(x)/(x^2 - pi^2)
Unión de expresiones racionales [src] 
  2       
pi *sin(x)
----------
   2    2 
 pi  - x
$$\frac{\pi^{2} \sin{\left(x \right)}}{- x^{2} + \pi^{2}}$$ 
pi^2*sin(x)/(pi^2 - x^2)
Combinatoria [src] 
      2          
   -pi *sin(x)   
-----------------
(pi + x)*(x - pi)
$$- \frac{\pi^{2} \sin{\left(x \right)}}{\left(x - \pi\right) \left(x + \pi\right)}$$ 
-pi^2*sin(x)/((pi + x)*(x - pi))
Potencias [src] 
   /   -I*x    I*x\ 
-I*\- e     + e   / 
--------------------
      /      2\     
      |     x |     
    2*|1 - ---|     
      |      2|     
      \    pi /
$$- \frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(- \frac{x^{2}}{\pi^{2}} + 1\right)}$$ 
-i*(-exp(-i*x) + exp(i*x))/(2*(1 - x^2/pi^2))
Parte trigonométrica [src] 
       1        
----------------
/      2\       
|     x |       
|1 - ---|*csc(x)
|      2|       
\    pi /
$$\frac{1}{\left(- \frac{x^{2}}{\pi^{2}} + 1\right) \csc{\left(x \right)}}$$ 
             /x\       
        2*tan|-|       
             \2/       
-----------------------
              /      2\
/       2/x\\ |     x |
|1 + tan |-||*|1 - ---|
\        \2// |      2|
              \    pi /
$$\frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(- \frac{x^{2}}{\pi^{2}} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$ 
   /    pi\
cos|x - --|
   \    2 /
-----------
        2  
       x   
  1 - ---  
        2  
      pi
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{- \frac{x^{2}}{\pi^{2}} + 1}$$ 
             /x\       
        2*cot|-|       
             \2/       
-----------------------
              /      2\
/       2/x\\ |     x |
|1 + cot |-||*|1 - ---|
\        \2// |      2|
              \    pi /
$$\frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(- \frac{x^{2}}{\pi^{2}} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$ 
          1          
---------------------
/      2\            
|     x |    /    pi\
|1 - ---|*sec|x - --|
|      2|    \    2 /
\    pi /
$$\frac{1}{\left(- \frac{x^{2}}{\pi^{2}} + 1\right) \sec{\left(x - \frac{\pi}{2} \right)}}$$ 
1/((1 - x^2/pi^2)*sec(x - pi/2))
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