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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(2*x)/(28*cos(2*x)-sin(2*x))

¿Cómo vas a descomponer esta sin(2*x)/(28*cos(2*x)-sin(2*x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
       sin(2*x)       
----------------------
28*cos(2*x) - sin(2*x)
sin⁡(2x)−sin⁡(2x)+28cos⁡(2x)\frac{\sin{\left(2 x \right)}}{- \sin{\left(2 x \right)} + 28 \cos{\left(2 x \right)}} 
sin(2*x)/(28*cos(2*x) - sin(2*x))
Respuesta numérica [src] 
sin(2*x)/(-sin(2*x) + 28.0*cos(2*x))
sin(2*x)/(-sin(2*x) + 28.0*cos(2*x))
Potencias [src] 
                 /   -2*I*x    2*I*x\              
              -I*\- e       + e     /              
---------------------------------------------------
  /                           /   -2*I*x    2*I*x\\
  |    -2*I*x       2*I*x   I*\- e       + e     /|
2*|14*e       + 14*e      + ----------------------|
  \                                   2           /
−i(e2ix−e−2ix)2(i(e2ix−e−2ix)2+14e2ix+14e−2ix)- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2 \left(\frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2} + 14 e^{2 i x} + 14 e^{- 2 i x}\right)} 
-i*(-exp(-2*i*x) + exp(2*i*x))/(2*(14*exp(-2*i*x) + 14*exp(2*i*x) + i*(-exp(-2*i*x) + exp(2*i*x))/2))
Abrimos la expresión [src] 
         2*cos(x)*sin(x)          
----------------------------------
            2                     
-28 + 56*cos (x) - 2*cos(x)*sin(x)
2sin⁡(x)cos⁡(x)−2sin⁡(x)cos⁡(x)+56cos⁡2(x)−28\frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{- 2 \sin{\left(x \right)} \cos{\left(x \right)} + 56 \cos^{2}{\left(x \right)} - 28} 
2*cos(x)*sin(x)/(-28 + 56*cos(x)^2 - 2*cos(x)*sin(x))
Parte trigonométrica [src] 
                   -2*tan(x)                    
------------------------------------------------
              /     /       2   \              \
/       2   \ |  28*\1 - tan (x)/     2*tan(x) |
\1 + tan (x)/*|- ---------------- + -----------|
              |           2                2   |
              \    1 + tan (x)      1 + tan (x)/
−2tan⁡(x)(−28(1−tan⁡2(x))tan⁡2(x)+1+2tan⁡(x)tan⁡2(x)+1)(tan⁡2(x)+1)- \frac{2 \tan{\left(x \right)}}{\left(- \frac{28 \left(1 - \tan^{2}{\left(x \right)}\right)}{\tan^{2}{\left(x \right)} + 1} + \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)} 
           /      pi\        
        cos|2*x - --|        
           \      2 /        
-----------------------------
     /      pi\              
- cos|2*x - --| + 28*cos(2*x)
     \      2 /
cos⁡(2x−π2)28cos⁡(2x)−cos⁡(2x−π2)\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{28 \cos{\left(2 x \right)} - \cos{\left(2 x - \frac{\pi}{2} \right)}} 
                     2*cot(x)                    
-------------------------------------------------
              /                   /        2   \\
/       2   \ |    2*cot(x)    28*\-1 + cot (x)/|
\1 + cot (x)/*|- ----------- + -----------------|
              |         2                2      |
              \  1 + cot (x)      1 + cot (x)   /
2cot⁡(x)(28(cot⁡2(x)−1)cot⁡2(x)+1−2cot⁡(x)cot⁡2(x)+1)(cot⁡2(x)+1)\frac{2 \cot{\left(x \right)}}{\left(\frac{28 \left(\cot^{2}{\left(x \right)} - 1\right)}{\cot^{2}{\left(x \right)} + 1} - \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)} 
          /      pi\        
      -cos|2*x - --|        
          \      2 /        
----------------------------
                  /      pi\
-28*cos(2*x) + cos|2*x - --|
                  \      2 /
−cos⁡(2x−π2)−28cos⁡(2x)+cos⁡(2x−π2)- \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{- 28 \cos{\left(2 x \right)} + \cos{\left(2 x - \frac{\pi}{2} \right)}} 
                    1                     
------------------------------------------
/        1            28   \    /      pi\
|- ------------- + --------|*sec|2*x - --|
|     /      pi\   sec(2*x)|    \      2 /
|  sec|2*x - --|           |              
\     \      2 /           /
1(−1sec⁡(2x−π2)+28sec⁡(2x))sec⁡(2x−π2)\frac{1}{\left(- \frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{28}{\sec{\left(2 x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}} 
       -sin(2*x)       
-----------------------
-28*cos(2*x) + sin(2*x)
−sin⁡(2x)sin⁡(2x)−28cos⁡(2x)- \frac{\sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 28 \cos{\left(2 x \right)}} 
          -sin(2*x)          
-----------------------------
        /pi      \           
- 28*sin|-- + 2*x| + sin(2*x)
        \2       /
−sin⁡(2x)sin⁡(2x)−28sin⁡(2x+π2)- \frac{\sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 28 \sin{\left(2 x + \frac{\pi}{2} \right)}} 
                    2*tan(x)                    
------------------------------------------------
              /                   /       2   \\
/       2   \ |    2*tan(x)    28*\1 - tan (x)/|
\1 + tan (x)/*|- ----------- + ----------------|
              |         2               2      |
              \  1 + tan (x)     1 + tan (x)   /
2tan⁡(x)(28(1−tan⁡2(x))tan⁡2(x)+1−2tan⁡(x)tan⁡2(x)+1)(tan⁡2(x)+1)\frac{2 \tan{\left(x \right)}}{\left(\frac{28 \left(1 - \tan^{2}{\left(x \right)}\right)}{\tan^{2}{\left(x \right)} + 1} - \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)} 
                  -1                    
----------------------------------------
/      1            28   \    /      pi\
|------------- - --------|*sec|2*x - --|
|   /      pi\   sec(2*x)|    \      2 /
|sec|2*x - --|           |              
\   \      2 /           /
−1(1sec⁡(2x−π2)−28sec⁡(2x))sec⁡(2x−π2)- \frac{1}{\left(\frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}} - \frac{28}{\sec{\left(2 x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}} 
                  1                  
-------------------------------------
/     1             28     \         
|- -------- + -------------|*csc(2*x)
|  csc(2*x)      /pi      \|         
|             csc|-- - 2*x||         
\                \2       //
1(28csc⁡(−2x+π2)−1csc⁡(2x))csc⁡(2x)\frac{1}{\left(\frac{28}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(2 x \right)}}\right) \csc{\left(2 x \right)}} 
               1                
--------------------------------
/     1          28   \         
|- -------- + --------|*csc(2*x)
\  csc(2*x)   sec(2*x)/
1(28sec⁡(2x)−1csc⁡(2x))csc⁡(2x)\frac{1}{\left(\frac{28}{\sec{\left(2 x \right)}} - \frac{1}{\csc{\left(2 x \right)}}\right) \csc{\left(2 x \right)}} 
                -1                 
-----------------------------------
/   1             28     \         
|-------- - -------------|*csc(2*x)
|csc(2*x)      /pi      \|         
|           csc|-- - 2*x||         
\              \2       //
−1(−28csc⁡(−2x+π2)+1csc⁡(2x))csc⁡(2x)- \frac{1}{\left(- \frac{28}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(2 x \right)}}\right) \csc{\left(2 x \right)}} 
                    -2*cot(x)                    
-------------------------------------------------
              /     /        2   \              \
/       2   \ |  28*\-1 + cot (x)/     2*cot(x) |
\1 + cot (x)/*|- ----------------- + -----------|
              |            2                2   |
              \     1 + cot (x)      1 + cot (x)/
−2cot⁡(x)(−28(cot⁡2(x)−1)cot⁡2(x)+1+2cot⁡(x)cot⁡2(x)+1)(cot⁡2(x)+1)- \frac{2 \cot{\left(x \right)}}{\left(- \frac{28 \left(\cot^{2}{\left(x \right)} - 1\right)}{\cot^{2}{\left(x \right)} + 1} + \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)} 
          sin(2*x)          
----------------------------
                  /pi      \
-sin(2*x) + 28*sin|-- + 2*x|
                  \2       /
sin⁡(2x)−sin⁡(2x)+28sin⁡(2x+π2)\frac{\sin{\left(2 x \right)}}{- \sin{\left(2 x \right)} + 28 \sin{\left(2 x + \frac{\pi}{2} \right)}} 
sin(2*x)/(-sin(2*x) + 28*sin(pi/2 + 2*x))
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