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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(2*x)/((5*sin(x)))

¿Cómo vas a descomponer esta sin(2*x)/((5*sin(x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(2*x)
--------
5*sin(x)
sin⁡(2x)5sin⁡(x)\frac{\sin{\left(2 x \right)}}{5 \sin{\left(x \right)}} 
sin(2*x)/((5*sin(x)))
Simplificación general [src] 
2*cos(x)
--------
   5
2cos⁡(x)5\frac{2 \cos{\left(x \right)}}{5} 
2*cos(x)/5
Potencias [src] 
   -2*I*x    2*I*x
- e       + e     
------------------
  /   -I*x    I*x\
5*\- e     + e   /
e2ix−e−2ix5(eix−e−ix)\frac{e^{2 i x} - e^{- 2 i x}}{5 \left(e^{i x} - e^{- i x}\right)} 
(-exp(-2*i*x) + exp(2*i*x))/(5*(-exp(-i*x) + exp(i*x)))
Respuesta numérica [src] 
0.2*sin(2*x)/sin(x)
0.2*sin(2*x)/sin(x)
Abrimos la expresión [src] 
2*cos(x)
--------
   5
2cos⁡(x)5\frac{2 \cos{\left(x \right)}}{5} 
2*cos(x)/5
Parte trigonométrica [src] 
  /       2/x\\
2*|1 - tan |-||
  \        \2//
---------------
  /       2/x\\
5*|1 + tan |-||
  \        \2//
2(1−tan⁡2(x2))5(tan⁡2(x2)+1)\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{5 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
  /        2/x\\
2*|-1 + cot |-||
  \         \2//
----------------
  /       2/x\\ 
5*|1 + cot |-|| 
  \        \2//
2(cot⁡2(x2)−1)5(cot⁡2(x2)+1)\frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{5 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
  csc(x)  
----------
5*csc(2*x)
csc⁡(x)5csc⁡(2x)\frac{\csc{\left(x \right)}}{5 \csc{\left(2 x \right)}} 
2*cos(x)
--------
   5
2cos⁡(x)5\frac{2 \cos{\left(x \right)}}{5} 
   /      pi\
cos|2*x - --|
   \      2 /
-------------
     /    pi\
5*cos|x - --|
     \    2 /
cos⁡(2x−π2)5cos⁡(x−π2)\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{5 \cos{\left(x - \frac{\pi}{2} \right)}} 
 /       2/x\\        
 |1 + tan |-||*tan(x) 
 \        \2//        
----------------------
  /       2   \    /x\
5*\1 + tan (x)/*tan|-|
                   \2/
(tan⁡2(x2)+1)tan⁡(x)5(tan⁡2(x)+1)tan⁡(x2)\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(x \right)}}{5 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}} 
 /       2/x\\        
 |1 + cot |-||*cot(x) 
 \        \2//        
----------------------
  /       2   \    /x\
5*\1 + cot (x)/*cot|-|
                   \2/
(cot⁡2(x2)+1)cot⁡(x)5(cot⁡2(x)+1)cot⁡(x2)\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(x \right)}}{5 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}} 
     /    pi\  
  sec|x - --|  
     \    2 /  
---------------
     /      pi\
5*sec|2*x - --|
     \      2 /
sec⁡(x−π2)5sec⁡(2x−π2)\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{5 \sec{\left(2 x - \frac{\pi}{2} \right)}} 
   2    
--------
5*sec(x)
25sec⁡(x)\frac{2}{5 \sec{\left(x \right)}} 
     /    pi\
2*sin|x + --|
     \    2 /
-------------
      5
2sin⁡(x+π2)5\frac{2 \sin{\left(x + \frac{\pi}{2} \right)}}{5} 
      2      
-------------
     /pi    \
5*csc|-- - x|
     \2     /
25csc⁡(−x+π2)\frac{2}{5 \csc{\left(- x + \frac{\pi}{2} \right)}} 
2/(5*csc(pi/2 - x))
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