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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   cos(2*t)*x           
--------------- - cos(t)
cos(t) + sin(x)
xcos⁡(2t)sin⁡(x)+cos⁡(t)−cos⁡(t)\frac{x \cos{\left(2 t \right)}}{\sin{\left(x \right)} + \cos{\left(t \right)}} - \cos{\left(t \right)} 
(cos(2*t)*x)/(cos(t) + sin(x)) - cos(t)
Simplificación general [src] 
x*cos(2*t) - (cos(t) + sin(x))*cos(t)
-------------------------------------
           cos(t) + sin(x)
xcos⁡(2t)−(sin⁡(x)+cos⁡(t))cos⁡(t)sin⁡(x)+cos⁡(t)\frac{x \cos{\left(2 t \right)} - \left(\sin{\left(x \right)} + \cos{\left(t \right)}\right) \cos{\left(t \right)}}{\sin{\left(x \right)} + \cos{\left(t \right)}} 
(x*cos(2*t) - (cos(t) + sin(x))*cos(t))/(cos(t) + sin(x))
Respuesta numérica [src] 
-cos(t) + x*cos(2*t)/(cos(t) + sin(x))
-cos(t) + x*cos(2*t)/(cos(t) + sin(x))
Denominador racional [src] 
x*cos(2*t) - (cos(t) + sin(x))*cos(t)
-------------------------------------
           cos(t) + sin(x)
xcos⁡(2t)−(sin⁡(x)+cos⁡(t))cos⁡(t)sin⁡(x)+cos⁡(t)\frac{x \cos{\left(2 t \right)} - \left(\sin{\left(x \right)} + \cos{\left(t \right)}\right) \cos{\left(t \right)}}{\sin{\left(x \right)} + \cos{\left(t \right)}} 
(x*cos(2*t) - (cos(t) + sin(x))*cos(t))/(cos(t) + sin(x))
Potencias [src] 
                          / -2*I*t    2*I*t\      
                          |e         e     |      
   I*t    -I*t          x*|------- + ------|      
  e      e                \   2        2   /      
- ---- - ----- + ---------------------------------
   2       2      I*t    -I*t     /   -I*x    I*x\
                 e      e       I*\- e     + e   /
                 ---- + ----- - ------------------
                  2       2             2
x(e2it2+e−2it2)−i(eix−e−ix)2+eit2+e−it2−eit2−e−it2\frac{x \left(\frac{e^{2 i t}}{2} + \frac{e^{- 2 i t}}{2}\right)}{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + \frac{e^{i t}}{2} + \frac{e^{- i t}}{2}} - \frac{e^{i t}}{2} - \frac{e^{- i t}}{2} 
-exp(i*t)/2 - exp(-i*t)/2 + x*(exp(-2*i*t)/2 + exp(2*i*t)/2)/(exp(i*t)/2 + exp(-i*t)/2 - i*(-exp(-i*x) + exp(i*x))/2)
Unión de expresiones racionales [src] 
x*cos(2*t) - (cos(t) + sin(x))*cos(t)
-------------------------------------
           cos(t) + sin(x)
xcos⁡(2t)−(sin⁡(x)+cos⁡(t))cos⁡(t)sin⁡(x)+cos⁡(t)\frac{x \cos{\left(2 t \right)} - \left(\sin{\left(x \right)} + \cos{\left(t \right)}\right) \cos{\left(t \right)}}{\sin{\left(x \right)} + \cos{\left(t \right)}} 
(x*cos(2*t) - (cos(t) + sin(x))*cos(t))/(cos(t) + sin(x))
Abrimos la expresión [src] 
                                     2     
                 x            2*x*cos (t)  
-cos(t) - --------------- + ---------------
          cos(t) + sin(x)   cos(t) + sin(x)
2xcos⁡2(t)sin⁡(x)+cos⁡(t)−xsin⁡(x)+cos⁡(t)−cos⁡(t)\frac{2 x \cos^{2}{\left(t \right)}}{\sin{\left(x \right)} + \cos{\left(t \right)}} - \frac{x}{\sin{\left(x \right)} + \cos{\left(t \right)}} - \cos{\left(t \right)} 
-cos(t) - x/(cos(t) + sin(x)) + 2*x*cos(t)^2/(cos(t) + sin(x))
Parte trigonométrica [src] 
          2/t\                                             
  -1 + cot |-|                  /        2   \             
           \2/                x*\-1 + cot (t)/             
- ------------ + ------------------------------------------
         2/t\                  /        2/t\          /x\ \
  1 + cot |-|                  |-1 + cot |-|     2*cot|-| |
          \2/    /       2   \ |         \2/          \2/ |
                 \1 + cot (t)/*|------------ + -----------|
                               |       2/t\           2/x\|
                               |1 + cot |-|    1 + cot |-||
                               \        \2/            \2//
x(cot⁡2(t)−1)(cot⁡2(t2)−1cot⁡2(t2)+1+2cot⁡(x2)cot⁡2(x2)+1)(cot⁡2(t)+1)−cot⁡2(t2)−1cot⁡2(t2)+1\frac{x \left(\cot^{2}{\left(t \right)} - 1\right)}{\left(\frac{\cot^{2}{\left(\frac{t}{2} \right)} - 1}{\cot^{2}{\left(\frac{t}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(t \right)} + 1\right)} - \frac{\cot^{2}{\left(\frac{t}{2} \right)} - 1}{\cot^{2}{\left(\frac{t}{2} \right)} + 1} 
    1                     x               
- ------ + -------------------------------
  sec(t)   /  1           1     \         
           |------ + -----------|*sec(2*t)
           |sec(t)      /    pi\|         
           |         sec|x - --||         
           \            \    2 //
x(1sec⁡(x−π2)+1sec⁡(t))sec⁡(2t)−1sec⁡(t)\frac{x}{\left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(t \right)}}\right) \sec{\left(2 t \right)}} - \frac{1}{\sec{\left(t \right)}} 
                       /pi      \   
                  x*sin|-- + 2*t|   
     /    pi\          \2       /   
- sin|t + --| + --------------------
     \    2 /               /    pi\
                sin(x) + sin|t + --|
                            \    2 /
xsin⁡(2t+π2)sin⁡(x)+sin⁡(t+π2)−sin⁡(t+π2)\frac{x \sin{\left(2 t + \frac{\pi}{2} \right)}}{\sin{\left(x \right)} + \sin{\left(t + \frac{\pi}{2} \right)}} - \sin{\left(t + \frac{\pi}{2} \right)} 
         2/t\                                            
  1 - tan |-|                  /       2   \             
          \2/                x*\1 - tan (t)/             
- ----------- + -----------------------------------------
         2/t\                 /       2/t\          /x\ \
  1 + tan |-|                 |1 - tan |-|     2*tan|-| |
          \2/   /       2   \ |        \2/          \2/ |
                \1 + tan (t)/*|----------- + -----------|
                              |       2/t\          2/x\|
                              |1 + tan |-|   1 + tan |-||
                              \        \2/           \2//
x(1−tan⁡2(t))(1−tan⁡2(t2)tan⁡2(t2)+1+2tan⁡(x2)tan⁡2(x2)+1)(tan⁡2(t)+1)−1−tan⁡2(t2)tan⁡2(t2)+1\frac{x \left(1 - \tan^{2}{\left(t \right)}\right)}{\left(\frac{1 - \tan^{2}{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(\frac{t}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(t \right)} + 1\right)} - \frac{1 - \tan^{2}{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(\frac{t}{2} \right)} + 1} 
               x*cos(2*t)     
-cos(t) + --------------------
                      /    pi\
          cos(t) + cos|x - --|
                      \    2 /
xcos⁡(2t)cos⁡(t)+cos⁡(x−π2)−cos⁡(t)\frac{x \cos{\left(2 t \right)}}{\cos{\left(t \right)} + \cos{\left(x - \frac{\pi}{2} \right)}} - \cos{\left(t \right)} 
    1                  x             
- ------ + --------------------------
  sec(t)   /  1        1   \         
           |------ + ------|*sec(2*t)
           \csc(x)   sec(t)/
x(1sec⁡(t)+1csc⁡(x))sec⁡(2t)−1sec⁡(t)\frac{x}{\left(\frac{1}{\sec{\left(t \right)}} + \frac{1}{\csc{\left(x \right)}}\right) \sec{\left(2 t \right)}} - \frac{1}{\sec{\left(t \right)}} 
       1                         x                  
- ----------- + ------------------------------------
     /pi    \   /  1           1     \    /pi      \
  csc|-- - t|   |------ + -----------|*csc|-- - 2*t|
     \2     /   |csc(x)      /pi    \|    \2       /
                |         csc|-- - t||              
                \            \2     //
x(1csc⁡(−t+π2)+1csc⁡(x))csc⁡(−2t+π2)−1csc⁡(−t+π2)\frac{x}{\left(\frac{1}{\csc{\left(- t + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(x \right)}}\right) \csc{\left(- 2 t + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(- t + \frac{\pi}{2} \right)}} 
-1/csc(pi/2 - t) + x/((1/csc(x) + 1/csc(pi/2 - t))*csc(pi/2 - 2*t))
Combinatoria [src] 
     2                                
- cos (t) + x*cos(2*t) - cos(t)*sin(x)
--------------------------------------
           cos(t) + sin(x)
xcos⁡(2t)−sin⁡(x)cos⁡(t)−cos⁡2(t)sin⁡(x)+cos⁡(t)\frac{x \cos{\left(2 t \right)} - \sin{\left(x \right)} \cos{\left(t \right)} - \cos^{2}{\left(t \right)}}{\sin{\left(x \right)} + \cos{\left(t \right)}} 
(-cos(t)^2 + x*cos(2*t) - cos(t)*sin(x))/(cos(t) + sin(x))
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