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¿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)
$$\frac{\sin{\left(2 x \right)}}{5 \sin{\left(x \right)}}$$
sin(2*x)/((5*sin(x)))
Simplificación general [src]
2*cos(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   /
$$\frac{e^{2 i x} - e^{- 2 i x}}{5 \left(e^{i x} - e^{- i x}\right)}$$
(-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    
$$\frac{2 \cos{\left(x \right)}}{5}$$
2*cos(x)/5
Parte trigonométrica [src]
  /       2/x\\
2*|1 - tan |-||
  \        \2//
---------------
  /       2/x\\
5*|1 + tan |-||
  \        \2//
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{5 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
  /        2/x\\
2*|-1 + cot |-||
  \         \2//
----------------
  /       2/x\\ 
5*|1 + cot |-|| 
  \        \2// 
$$\frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{5 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
  csc(x)  
----------
5*csc(2*x)
$$\frac{\csc{\left(x \right)}}{5 \csc{\left(2 x \right)}}$$
2*cos(x)
--------
   5    
$$\frac{2 \cos{\left(x \right)}}{5}$$
   /      pi\
cos|2*x - --|
   \      2 /
-------------
     /    pi\
5*cos|x - --|
     \    2 /
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{5 \cos{\left(x - \frac{\pi}{2} \right)}}$$
 /       2/x\\        
 |1 + tan |-||*tan(x) 
 \        \2//        
----------------------
  /       2   \    /x\
5*\1 + tan (x)/*tan|-|
                   \2/
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(x \right)}}{5 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}$$
 /       2/x\\        
 |1 + cot |-||*cot(x) 
 \        \2//        
----------------------
  /       2   \    /x\
5*\1 + cot (x)/*cot|-|
                   \2/
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(x \right)}}{5 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}$$
     /    pi\  
  sec|x - --|  
     \    2 /  
---------------
     /      pi\
5*sec|2*x - --|
     \      2 /
$$\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{5 \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
   2    
--------
5*sec(x)
$$\frac{2}{5 \sec{\left(x \right)}}$$
     /    pi\
2*sin|x + --|
     \    2 /
-------------
      5      
$$\frac{2 \sin{\left(x + \frac{\pi}{2} \right)}}{5}$$
      2      
-------------
     /pi    \
5*csc|-- - x|
     \2     /
$$\frac{2}{5 \csc{\left(- x + \frac{\pi}{2} \right)}}$$
2/(5*csc(pi/2 - x))