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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(-2+x/2)/2-1/(2*tan(-2+x/2))

¿Cómo vas a descomponer esta tan(-2+x/2)/2-1/(2*tan(-2+x/2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /     x\                
tan|-2 + -|                
   \     2/         1      
----------- - -------------
     2             /     x\
              2*tan|-2 + -|
                   \     2/
tan⁡(x2−2)2−12tan⁡(x2−2)\frac{\tan{\left(\frac{x}{2} - 2 \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} - 2 \right)}} 
tan(-2 + x/2)/2 - 1/(2*tan(-2 + x/2))
Descomposición de una fracción [src] 
tan(-2 + x/2)/2 - 1/(2*tan(-2 + x/2))
tan⁡(x2−2)2−12tan⁡(x2−2)\frac{\tan{\left(\frac{x}{2} - 2 \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} - 2 \right)}} 
   /     x\                
tan|-2 + -|                
   \     2/         1      
----------- - -------------
     2             /     x\
              2*tan|-2 + -|
                   \     2/
Simplificación general [src] 
        2/     x\
-1 + tan |-2 + -|
         \     2/
-----------------
       /     x\  
  2*tan|-2 + -|  
       \     2/
tan⁡2(x2−2)−12tan⁡(x2−2)\frac{\tan^{2}{\left(\frac{x}{2} - 2 \right)} - 1}{2 \tan{\left(\frac{x}{2} - 2 \right)}} 
(-1 + tan(-2 + x/2)^2)/(2*tan(-2 + x/2))
Respuesta numérica [src] 
0.5*tan(-2 + x/2) - 0.5/tan(-2 + x/2)
0.5*tan(-2 + x/2) - 0.5/tan(-2 + x/2)
Combinatoria [src] 
/       /     x\\ /        /     x\\
|1 + tan|-2 + -||*|-1 + tan|-2 + -||
\       \     2// \        \     2//
------------------------------------
                /     x\            
           2*tan|-2 + -|            
                \     2/
(tan⁡(x2−2)−1)(tan⁡(x2−2)+1)2tan⁡(x2−2)\frac{\left(\tan{\left(\frac{x}{2} - 2 \right)} - 1\right) \left(\tan{\left(\frac{x}{2} - 2 \right)} + 1\right)}{2 \tan{\left(\frac{x}{2} - 2 \right)}} 
(1 + tan(-2 + x/2))*(-1 + tan(-2 + x/2))/(2*tan(-2 + x/2))
Denominador racional [src] 
          2/     x\
-2 + 2*tan |-2 + -|
           \     2/
-------------------
        /     x\   
   4*tan|-2 + -|   
        \     2/
2tan⁡2(x2−2)−24tan⁡(x2−2)\frac{2 \tan^{2}{\left(\frac{x}{2} - 2 \right)} - 2}{4 \tan{\left(\frac{x}{2} - 2 \right)}} 
(-2 + 2*tan(-2 + x/2)^2)/(4*tan(-2 + x/2))
Unión de expresiones racionales [src] 
        2/-4 + x\
-1 + tan |------|
         \  2   /
-----------------
       /-4 + x\  
  2*tan|------|  
       \  2   /
tan⁡2(x−42)−12tan⁡(x−42)\frac{\tan^{2}{\left(\frac{x - 4}{2} \right)} - 1}{2 \tan{\left(\frac{x - 4}{2} \right)}} 
(-1 + tan((-4 + x)/2)^2)/(2*tan((-4 + x)/2))
Potencias [src] 
   /   /     x\      /    x\\      /     /     x\      /    x\\
   | I*|-2 + -|    I*|2 - -||      |   I*|-2 + -|    I*|2 - -||
   |   \     2/      \    2/|      |     \     2/      \    2/|
 I*\e           + e         /    I*\- e           + e         /
------------------------------ + ------------------------------
  /     /     x\      /    x\\      /   /     x\      /    x\\ 
  |   I*|-2 + -|    I*|2 - -||      | I*|-2 + -|    I*|2 - -|| 
  |     \     2/      \    2/|      |   \     2/      \    2/| 
2*\- e           + e         /    2*\e           + e         /
i(ei(2−x2)−ei(x2−2))2(ei(2−x2)+ei(x2−2))+i(ei(2−x2)+ei(x2−2))2(ei(2−x2)−ei(x2−2))\frac{i \left(e^{i \left(2 - \frac{x}{2}\right)} - e^{i \left(\frac{x}{2} - 2\right)}\right)}{2 \left(e^{i \left(2 - \frac{x}{2}\right)} + e^{i \left(\frac{x}{2} - 2\right)}\right)} + \frac{i \left(e^{i \left(2 - \frac{x}{2}\right)} + e^{i \left(\frac{x}{2} - 2\right)}\right)}{2 \left(e^{i \left(2 - \frac{x}{2}\right)} - e^{i \left(\frac{x}{2} - 2\right)}\right)} 
i*(exp(i*(-2 + x/2)) + exp(i*(2 - x/2)))/(2*(-exp(i*(-2 + x/2)) + exp(i*(2 - x/2)))) + i*(-exp(i*(-2 + x/2)) + exp(i*(2 - x/2)))/(2*(exp(i*(-2 + x/2)) + exp(i*(2 - x/2))))
Abrimos la expresión [src] 
                                    /x\                                               /x\    
                                 tan|-|                                     tan(2)*tan|-|    
           1                        \2/                  tan(2)                       \2/    
- -------------------- + --------------------- - --------------------- - --------------------
    /             /x\\     /              /x\\     /              /x\\     /             /x\\
  2*|-tan(2) + tan|-||   2*|1 + tan(2)*tan|-||   2*|1 + tan(2)*tan|-||   2*|-tan(2) + tan|-||
    \             \2//     \              \2//     \              \2//     \             \2//
−tan⁡(2)tan⁡(x2)2(tan⁡(x2)−tan⁡(2))−12(tan⁡(x2)−tan⁡(2))+tan⁡(x2)2(tan⁡(2)tan⁡(x2)+1)−tan⁡(2)2(tan⁡(2)tan⁡(x2)+1)- \frac{\tan{\left(2 \right)} \tan{\left(\frac{x}{2} \right)}}{2 \left(\tan{\left(\frac{x}{2} \right)} - \tan{\left(2 \right)}\right)} - \frac{1}{2 \left(\tan{\left(\frac{x}{2} \right)} - \tan{\left(2 \right)}\right)} + \frac{\tan{\left(\frac{x}{2} \right)}}{2 \left(\tan{\left(2 \right)} \tan{\left(\frac{x}{2} \right)} + 1\right)} - \frac{\tan{\left(2 \right)}}{2 \left(\tan{\left(2 \right)} \tan{\left(\frac{x}{2} \right)} + 1\right)} 
-1/(2*(-tan(2) + tan(x/2))) + tan(x/2)/(2*(1 + tan(2)*tan(x/2))) - tan(2)/(2*(1 + tan(2)*tan(x/2))) - tan(2)*tan(x/2)/(2*(-tan(2) + tan(x/2)))
Parte trigonométrica [src] 
    /     x\        /     x\ 
 sec|-2 + -|     csc|-2 + -| 
    \     2/        \     2/ 
------------- - -------------
     /     x\        /     x\
2*csc|-2 + -|   2*sec|-2 + -|
     \     2/        \     2/
−csc⁡(x2−2)2sec⁡(x2−2)+sec⁡(x2−2)2csc⁡(x2−2)- \frac{\csc{\left(\frac{x}{2} - 2 \right)}}{2 \sec{\left(\frac{x}{2} - 2 \right)}} + \frac{\sec{\left(\frac{x}{2} - 2 \right)}}{2 \csc{\left(\frac{x}{2} - 2 \right)}} 
    /         pi\ 
-sec|-4 + x - --| 
    \         2 / 
------------------
   sec(-4 + x)
−sec⁡(x−4−π2)sec⁡(x−4)- \frac{\sec{\left(x - 4 - \frac{\pi}{2} \right)}}{\sec{\left(x - 4 \right)}} 
    -1     
-----------
tan(-4 + x)
−1tan⁡(x−4)- \frac{1}{\tan{\left(x - 4 \right)}} 
-cot(-4 + x)
−cot⁡(x−4)- \cot{\left(x - 4 \right)} 
   2/     x\                 
sin |-2 + -|                 
    \     2/    sin(-4 + x)  
------------ - --------------
sin(-4 + x)         2/     x\
               4*sin |-2 + -|
                     \     2/
sin⁡2(x2−2)sin⁡(x−4)−sin⁡(x−4)4sin⁡2(x2−2)\frac{\sin^{2}{\left(\frac{x}{2} - 2 \right)}}{\sin{\left(x - 4 \right)}} - \frac{\sin{\left(x - 4 \right)}}{4 \sin^{2}{\left(\frac{x}{2} - 2 \right)}} 
   /    pi   x\         /     x\   
csc|2 + -- - -|      csc|-2 + -|   
   \    2    2/         \     2/   
--------------- - -----------------
      /     x\         /    pi   x\
 2*csc|-2 + -|    2*csc|2 + -- - -|
      \     2/         \    2    2/
−csc⁡(x2−2)2csc⁡(−x2+π2+2)+csc⁡(−x2+π2+2)2csc⁡(x2−2)- \frac{\csc{\left(\frac{x}{2} - 2 \right)}}{2 \csc{\left(- \frac{x}{2} + \frac{\pi}{2} + 2 \right)}} + \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} + 2 \right)}}{2 \csc{\left(\frac{x}{2} - 2 \right)}} 
   /     x   pi\         /     x\    
cos|-2 + - - --|      cos|-2 + -|    
   \     2   2 /         \     2/    
---------------- - ------------------
      /     x\          /     x   pi\
 2*cos|-2 + -|     2*cos|-2 + - - --|
      \     2/          \     2   2 /
−cos⁡(x2−2)2cos⁡(x2−2−π2)+cos⁡(x2−2−π2)2cos⁡(x2−2)- \frac{\cos{\left(\frac{x}{2} - 2 \right)}}{2 \cos{\left(\frac{x}{2} - 2 - \frac{\pi}{2} \right)}} + \frac{\cos{\left(\frac{x}{2} - 2 - \frac{\pi}{2} \right)}}{2 \cos{\left(\frac{x}{2} - 2 \right)}} 
 -csc(-4 + x)  
---------------
   /    pi    \
csc|4 + -- - x|
   \    2     /
−csc⁡(x−4)csc⁡(−x+π2+4)- \frac{\csc{\left(x - 4 \right)}}{\csc{\left(- x + \frac{\pi}{2} + 4 \right)}} 
                   /     x\
                cot|-2 + -|
      1            \     2/
------------- - -----------
     /     x\        2     
2*cot|-2 + -|              
     \     2/
−cot⁡(x2−2)2+12cot⁡(x2−2)- \frac{\cot{\left(\frac{x}{2} - 2 \right)}}{2} + \frac{1}{2 \cot{\left(\frac{x}{2} - 2 \right)}} 
    /     x\        /     x\ 
 sin|-2 + -|     cos|-2 + -| 
    \     2/        \     2/ 
------------- - -------------
     /     x\        /     x\
2*cos|-2 + -|   2*sin|-2 + -|
     \     2/        \     2/
sin⁡(x2−2)2cos⁡(x2−2)−cos⁡(x2−2)2sin⁡(x2−2)\frac{\sin{\left(\frac{x}{2} - 2 \right)}}{2 \cos{\left(\frac{x}{2} - 2 \right)}} - \frac{\cos{\left(\frac{x}{2} - 2 \right)}}{2 \sin{\left(\frac{x}{2} - 2 \right)}} 
-sin(-8 + 2*x) 
---------------
      2        
 2*sin (-4 + x)
−sin⁡(2x−8)2sin⁡2(x−4)- \frac{\sin{\left(2 x - 8 \right)}}{2 \sin^{2}{\left(x - 4 \right)}} 
   /     x\      /     x\
tan|-2 + -|   cot|-2 + -|
   \     2/      \     2/
----------- - -----------
     2             2
tan⁡(x2−2)2−cot⁡(x2−2)2\frac{\tan{\left(\frac{x}{2} - 2 \right)}}{2} - \frac{\cot{\left(\frac{x}{2} - 2 \right)}}{2} 
 -cos(-4 + x)   
----------------
   /         pi\
cos|-4 + x - --|
   \         2 /
−cos⁡(x−4)cos⁡(x−4−π2)- \frac{\cos{\left(x - 4 \right)}}{\cos{\left(x - 4 - \frac{\pi}{2} \right)}} 
      /     x\          /     x   pi\
   sec|-2 + -|       sec|-2 + - - --|
      \     2/          \     2   2 /
------------------ - ----------------
     /     x   pi\         /     x\  
2*sec|-2 + - - --|    2*sec|-2 + -|  
     \     2   2 /         \     2/
sec⁡(x2−2)2sec⁡(x2−2−π2)−sec⁡(x2−2−π2)2sec⁡(x2−2)\frac{\sec{\left(\frac{x}{2} - 2 \right)}}{2 \sec{\left(\frac{x}{2} - 2 - \frac{\pi}{2} \right)}} - \frac{\sec{\left(\frac{x}{2} - 2 - \frac{\pi}{2} \right)}}{2 \sec{\left(\frac{x}{2} - 2 \right)}} 
sec(-2 + x/2)/(2*sec(-2 + x/2 - pi/2)) - sec(-2 + x/2 - pi/2)/(2*sec(-2 + x/2))
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