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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(x/2)/(x^2+x-2)

¿Cómo vas a descomponer esta tan(x/2)/(x^2+x-2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     /x\  
  tan|-|  
     \2/  
----------
 2        
x  + x - 2
tan⁡(x2)(x2+x)−2\frac{\tan{\left(\frac{x}{2} \right)}}{\left(x^{2} + x\right) - 2} 
tan(x/2)/(x^2 + x - 2)
Simplificación general [src] 
      /x\  
   tan|-|  
      \2/  
-----------
          2
-2 + x + x
tan⁡(x2)x2+x−2\frac{\tan{\left(\frac{x}{2} \right)}}{x^{2} + x - 2} 
tan(x/2)/(-2 + x + x^2)
Respuesta numérica [src] 
tan(x/2)/(-2.0 + x + x^2)
tan(x/2)/(-2.0 + x + x^2)
Combinatoria [src] 
        /x\     
     tan|-|     
        \2/     
----------------
(-1 + x)*(2 + x)
tan⁡(x2)(x−1)(x+2)\frac{\tan{\left(\frac{x}{2} \right)}}{\left(x - 1\right) \left(x + 2\right)} 
tan(x/2)/((-1 + x)*(2 + x))
Denominador racional [src] 
      /x\  
   tan|-|  
      \2/  
-----------
          2
-2 + x + x
tan⁡(x2)x2+x−2\frac{\tan{\left(\frac{x}{2} \right)}}{x^{2} + x - 2} 
tan(x/2)/(-2 + x + x^2)
Denominador común [src] 
      /x\  
   tan|-|  
      \2/  
-----------
          2
-2 + x + x
tan⁡(x2)x2+x−2\frac{\tan{\left(\frac{x}{2} \right)}}{x^{2} + x - 2} 
tan(x/2)/(-2 + x + x^2)
Unión de expresiones racionales [src] 
       /x\    
    tan|-|    
       \2/    
--------------
-2 + x*(1 + x)
tan⁡(x2)x(x+1)−2\frac{\tan{\left(\frac{x}{2} \right)}}{x \left(x + 1\right) - 2} 
tan(x/2)/(-2 + x*(1 + x))
Potencias [src] 
       /   I*x    -I*x \     
       |   ---    -----|     
       |    2       2  |     
     I*\- e    + e     /     
-----------------------------
/ I*x    -I*x \              
| ---    -----|              
|  2       2  | /          2\
\e    + e     /*\-2 + x + x /
i(−eix2+e−ix2)(eix2+e−ix2)(x2+x−2)\frac{i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right) \left(x^{2} + x - 2\right)} 
      /x\  
   tan|-|  
      \2/  
-----------
          2
-2 + x + x
tan⁡(x2)x2+x−2\frac{\tan{\left(\frac{x}{2} \right)}}{x^{2} + x - 2} 
tan(x/2)/(-2 + x + x^2)
Compilar la expresión [src] 
      /x\  
   tan|-|  
      \2/  
-----------
          2
-2 + x + x
tan⁡(x2)x2+x−2\frac{\tan{\left(\frac{x}{2} \right)}}{x^{2} + x - 2} 
tan(x/2)/(-2 + x + x^2)
Parte trigonométrica [src] 
           2/x   pi\     
      2*cos |- - --|     
            \2   2 /     
-------------------------
/          2\    /    pi\
\-2 + x + x /*cos|x - --|
                 \    2 /
2cos⁡2(x2−π2)(x2+x−2)cos⁡(x−π2)\frac{2 \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(x^{2} + x - 2\right) \cos{\left(x - \frac{\pi}{2} \right)}} 
       2*csc(x)      
---------------------
/          2\    2/x\
\-2 + x + x /*csc |-|
                  \2/
2csc⁡(x)(x2+x−2)csc⁡2(x2)\frac{2 \csc{\left(x \right)}}{\left(x^{2} + x - 2\right) \csc^{2}{\left(\frac{x}{2} \right)}} 
         1          
--------------------
/          2\    /x\
\-2 + x + x /*cot|-|
                 \2/
1(x2+x−2)cot⁡(x2)\frac{1}{\left(x^{2} + x - 2\right) \cot{\left(\frac{x}{2} \right)}} 
      /x\  
   tan|-|  
      \2/  
-----------
          2
-2 + x + x
tan⁡(x2)x2+x−2\frac{\tan{\left(\frac{x}{2} \right)}}{x^{2} + x - 2} 
          /x\       
       sec|-|       
          \2/       
--------------------
/          2\    /x\
\-2 + x + x /*csc|-|
                 \2/
sec⁡(x2)(x2+x−2)csc⁡(x2)\frac{\sec{\left(\frac{x}{2} \right)}}{\left(x^{2} + x - 2\right) \csc{\left(\frac{x}{2} \right)}} 
           /    pi\       
      2*sec|x - --|       
           \    2 /       
--------------------------
/          2\    2/x   pi\
\-2 + x + x /*sec |- - --|
                  \2   2 /
2sec⁡(x−π2)(x2+x−2)sec⁡2(x2−π2)\frac{2 \sec{\left(x - \frac{\pi}{2} \right)}}{\left(x^{2} + x - 2\right) \sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} 
           2/x\ /       2/x\\      
      4*cot |-|*|1 + cot |-||      
            \4/ \        \2//      
-----------------------------------
             2                     
/       2/x\\  /          2\    /x\
|1 + cot |-|| *\-2 + x + x /*cot|-|
\        \4//                   \2/
4(cot⁡2(x2)+1)cot⁡2(x4)(cot⁡2(x4)+1)2(x2+x−2)cot⁡(x2)\frac{4 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot^{2}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \left(x^{2} + x - 2\right) \cot{\left(\frac{x}{2} \right)}} 
          /x\       
       sin|-|       
          \2/       
--------------------
/          2\    /x\
\-2 + x + x /*cos|-|
                 \2/
sin⁡(x2)(x2+x−2)cos⁡(x2)\frac{\sin{\left(\frac{x}{2} \right)}}{\left(x^{2} + x - 2\right) \cos{\left(\frac{x}{2} \right)}} 
       /x   pi\     
    cos|- - --|     
       \2   2 /     
--------------------
/          2\    /x\
\-2 + x + x /*cos|-|
                 \2/
cos⁡(x2−π2)(x2+x−2)cos⁡(x2)\frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(x^{2} + x - 2\right) \cos{\left(\frac{x}{2} \right)}} 
          2/x\      
     2*sin |-|      
           \2/      
--------------------
/          2\       
\-2 + x + x /*sin(x)
2sin⁡2(x2)(x2+x−2)sin⁡(x)\frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\left(x^{2} + x - 2\right) \sin{\left(x \right)}} 
           2/x\ /       2/x\\      
      4*tan |-|*|1 + tan |-||      
            \4/ \        \2//      
-----------------------------------
             2                     
/       2/x\\  /          2\    /x\
|1 + tan |-|| *\-2 + x + x /*tan|-|
\        \4//                   \2/
4(tan⁡2(x2)+1)tan⁡2(x4)(tan⁡2(x4)+1)2(x2+x−2)tan⁡(x2)\frac{4 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan^{2}{\left(\frac{x}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \left(x^{2} + x - 2\right) \tan{\left(\frac{x}{2} \right)}} 
             /x\         
          sec|-|         
             \2/         
-------------------------
/          2\    /x   pi\
\-2 + x + x /*sec|- - --|
                 \2   2 /
sec⁡(x2)(x2+x−2)sec⁡(x2−π2)\frac{\sec{\left(\frac{x}{2} \right)}}{\left(x^{2} + x - 2\right) \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} 
       /pi   x\     
    csc|-- - -|     
       \2    2/     
--------------------
/          2\    /x\
\-2 + x + x /*csc|-|
                 \2/
csc⁡(−x2+π2)(x2+x−2)csc⁡(x2)\frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\left(x^{2} + x - 2\right) \csc{\left(\frac{x}{2} \right)}} 
     2/x\       
2*sin |-|*csc(x)
      \2/       
----------------
            2   
  -2 + x + x
2sin⁡2(x2)csc⁡(x)x2+x−2\frac{2 \sin^{2}{\left(\frac{x}{2} \right)} \csc{\left(x \right)}}{x^{2} + x - 2} 
2*sin(x/2)^2*csc(x)/(-2 + x + x^2)
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