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(x*(x-1)^2)^(1/3)*((x-1)^2/3+x*(-2+2*x)/3)/(x*(x-1)^2)
(z-a)/(5*z-2*a)-(z-4*a)/(z)
((z)-(7*z/z+3))*((z+3)/(z-4))
z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z)
Factorizar el polinomio:
z^3+3*z^2
z^2-8*p*z-z+4*p+16*p^2
z^2-6*z+10
z^2+5*z-6
Descomponer al cuadrado:
y^4-y^2+9
y^4+y^2-8
-y^4+y^2+9
y^4-y^2-5
Expresiones idénticas
cos dos x-sin^ dos /(2sin^2-cosx)
coseno de 2x menos seno de al cuadrado dividir por (2 seno de al cuadrado menos coseno de x)
coseno de dos x menos seno de en el grado dos dividir por (2 seno de al cuadrado menos coseno de x)
cos2x-sin2/(2sin2-cosx)
cos2x-sin2/2sin2-cosx
cos2x-sin²/(2sin²-cosx)
cos2x-sin en el grado 2/(2sin en el grado 2-cosx)
cos2x-sin^2/2sin^2-cosx
cos2x-sin^2 dividir por (2sin^2-cosx)
Expresiones semejantes
cos2x+sin^2/(2sin^2-cosx)
cos2x-sin^2/(2sin^2+cosx)
Expresiones con funciones
Seno sin
sin(tan(x))/(1+x^2)+(1+tan(x)^2)*atan(x)*cos(tan(x))
sin^2(x)-cos^2(x)+cos^4(x)/(cos^2(x)-sin^2(x)+sin^4(x))
sin(2*a)/((2*tan(a)))
sin(2*x)/((17*sin(x)))
sin(2*x)/((21*sin(x)))

Simplificación de expresiones/ Descomposición en fracciones simples/ cos2x-sin^2/(2sin^2-cosx)

¿Cómo vas a descomponer esta cos2x-sin^2/(2sin^2-cosx) expresión en fracciones?

Solución

Ha introducido [src]

                   2         
                sin (x)      
cos(2*x) - ------------------
                2            
           2*sin (x) - cos(x)

$$\cos{\left(2 x \right)} - \frac{\sin^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - \cos{\left(x \right)}}$$

cos(2*x) - sin(x)^2/(2*sin(x)^2 - cos(x))

Simplificación general [src]

     2      /               2   \         
- sin (x) + \-cos(x) + 2*sin (x)/*cos(2*x)
------------------------------------------
                          2               
           -cos(x) + 2*sin (x)

$$\frac{\left(2 \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(2 x \right)} - \sin^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - \cos{\left(x \right)}}$$

(-sin(x)^2 + (-cos(x) + 2*sin(x)^2)*cos(2*x))/(-cos(x) + 2*sin(x)^2)

Respuesta numérica [src]

-sin(x)^2/(-cos(x) + 2.0*sin(x)^2) + cos(2*x)

-sin(x)^2/(-cos(x) + 2.0*sin(x)^2) + cos(2*x)

Denominador racional [src]

     2      /               2   \         
- sin (x) + \-cos(x) + 2*sin (x)/*cos(2*x)
------------------------------------------
                          2               
           -cos(x) + 2*sin (x)

$$\frac{\left(2 \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(2 x \right)} - \sin^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - \cos{\left(x \right)}}$$

(-sin(x)^2 + (-cos(x) + 2*sin(x)^2)*cos(2*x))/(-cos(x) + 2*sin(x)^2)

Potencias [src]

                                             2           
 -2*I*x    2*I*x             /   -I*x    I*x\            
e         e                  \- e     + e   /            
------- + ------ + --------------------------------------
   2        2        /                  2               \
                     |  /   -I*x    I*x\     I*x    -I*x|
                     |  \- e     + e   /    e      e    |
                   4*|- ----------------- - ---- - -----|
                     \          2            2       2  /

$$\frac{\left(e^{i x} - e^{- i x}\right)^{2}}{4 \left(- \frac{\left(e^{i x} - e^{- i x}\right)^{2}}{2} - \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}\right)} + \frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}$$

exp(-2*i*x)/2 + exp(2*i*x)/2 + (-exp(-i*x) + exp(i*x))^2/(4*(-(-exp(-i*x) + exp(i*x))^2/2 - exp(i*x)/2 - exp(-i*x)/2))

Combinatoria [src]

   2                             2            
sin (x) + cos(x)*cos(2*x) - 2*sin (x)*cos(2*x)
----------------------------------------------
                    2                         
             - 2*sin (x) + cos(x)

$$\frac{- 2 \sin^{2}{\left(x \right)} \cos{\left(2 x \right)} + \sin^{2}{\left(x \right)} + \cos{\left(x \right)} \cos{\left(2 x \right)}}{- 2 \sin^{2}{\left(x \right)} + \cos{\left(x \right)}}$$

(sin(x)^2 + cos(x)*cos(2*x) - 2*sin(x)^2*cos(2*x))/(-2*sin(x)^2 + cos(x))

Unión de expresiones racionales [src]

     2      /               2   \         
- sin (x) + \-cos(x) + 2*sin (x)/*cos(2*x)
------------------------------------------
                          2               
           -cos(x) + 2*sin (x)

$$\frac{\left(2 \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(2 x \right)} - \sin^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - \cos{\left(x \right)}}$$

(-sin(x)^2 + (-cos(x) + 2*sin(x)^2)*cos(2*x))/(-cos(x) + 2*sin(x)^2)

Abrimos la expresión [src]

                         2         
          2           sin (x)      
-1 + 2*cos (x) - ------------------
                      2            
                 2*sin (x) - cos(x)

$$2 \cos^{2}{\left(x \right)} - 1 - \frac{\sin^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - \cos{\left(x \right)}}$$

-1 + 2*cos(x)^2 - sin(x)^2/(2*sin(x)^2 - cos(x))

Denominador común [src]

         2                     
      sin (x)                  
-------------------- + cos(2*x)
       2                       
- 2*sin (x) + cos(x)

$$\cos{\left(2 x \right)} + \frac{\sin^{2}{\left(x \right)}}{- 2 \sin^{2}{\left(x \right)} + \cos{\left(x \right)}}$$

sin(x)^2/(-2*sin(x)^2 + cos(x)) + cos(2*x)

Parte trigonométrica [src]

        -1 + cos(2*x)                  
- -------------------------- + cos(2*x)
  2*(-1 + cos(x) + cos(2*x))

$$- \frac{\cos{\left(2 x \right)} - 1}{2 \left(\cos{\left(x \right)} + \cos{\left(2 x \right)} - 1\right)} + \cos{\left(2 x \right)}$$

           2/    pi\                 
        cos |x - --|                 
            \    2 /                 
- ------------------------ + cos(2*x)
                 2/    pi\           
  -cos(x) + 2*cos |x - --|           
                  \    2 /

$$\cos{\left(2 x \right)} - \frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{- \cos{\left(x \right)} + 2 \cos^{2}{\left(x - \frac{\pi}{2} \right)}}$$

                   /pi      \                         
           -1 + sin|-- + 2*x|                         
                   \2       /               /pi      \
- ------------------------------------ + sin|-- + 2*x|
    /        /    pi\      /pi      \\      \2       /
  2*|-1 + sin|x + --| + sin|-- + 2*x||                
    \        \    2 /      \2       //

$$- \frac{\sin{\left(2 x + \frac{\pi}{2} \right)} - 1}{2 \left(\sin{\left(x + \frac{\pi}{2} \right)} + \sin{\left(2 x + \frac{\pi}{2} \right)} - 1\right)} + \sin{\left(2 x + \frac{\pi}{2} \right)}$$

   1                    1              
-------- - ----------------------------
sec(2*x)   /    1         2   \    2   
           |- ------ + -------|*csc (x)
           |  sec(x)      2   |        
           \           csc (x)/

$$\frac{1}{\sec{\left(2 x \right)}} - \frac{1}{\left(- \frac{1}{\sec{\left(x \right)}} + \frac{2}{\csc^{2}{\left(x \right)}}\right) \csc^{2}{\left(x \right)}}$$

                                   2            
                            1 - tan (x)         
                       -1 + -----------         
       2                           2            
1 - tan (x)                 1 + tan (x)         
----------- - ----------------------------------
       2        /                          2/x\\
1 + tan (x)     |            2      1 - tan |-||
                |     1 - tan (x)           \2/|
              2*|-1 + ----------- + -----------|
                |            2             2/x\|
                |     1 + tan (x)   1 + tan |-||
                \                           \2//

$$\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} - \frac{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} - 1}{2 \left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} - 1\right)}$$

                                       2/x\                    
        2                         4*cot |-|                    
-1 + cot (x)                            \2/                    
------------ - ------------------------------------------------
       2                      /          2/x\          2/x\   \
1 + cot (x)                 2 |  -1 + cot |-|     8*cot |-|   |
               /       2/x\\  |           \2/           \2/   |
               |1 + cot |-|| *|- ------------ + --------------|
               \        \2//  |         2/x\                 2|
                              |  1 + cot |-|    /       2/x\\ |
                              |          \2/    |1 + cot |-|| |
                              \                 \        \2// /

$$\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} - \frac{4 \cot^{2}{\left(\frac{x}{2} \right)}}{\left(- \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{8 \cot^{2}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}$$

                                     2             
                             -1 + cot (x)          
                        -1 + ------------          
        2                           2              
-1 + cot (x)                 1 + cot (x)           
------------ - ------------------------------------
       2         /                            2/x\\
1 + cot (x)      |             2      -1 + cot |-||
                 |     -1 + cot (x)            \2/|
               2*|-1 + ------------ + ------------|
                 |            2              2/x\ |
                 |     1 + cot (x)    1 + cot |-| |
                 \                            \2/ /

$$- \frac{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} - 1}{2 \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} - 1\right)} + \frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}$$

                                      2/x\                   
       2                         4*tan |-|                   
1 - tan (x)                            \2/                   
----------- - -----------------------------------------------
       2                     /         2/x\          2/x\   \
1 + tan (x)                2 |  1 - tan |-|     8*tan |-|   |
              /       2/x\\  |          \2/           \2/   |
              |1 + tan |-|| *|- ----------- + --------------|
              \        \2//  |         2/x\                2|
                             |  1 + tan |-|   /       2/x\\ |
                             |          \2/   |1 + tan |-|| |
                             \                \        \2// /

$$\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} - \frac{4 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(- \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{8 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}$$

              2                            
           sin (x)               /pi      \
- ------------------------- + sin|-- + 2*x|
       /    pi\        2         \2       /
  - sin|x + --| + 2*sin (x)                
       \    2 /

$$\sin{\left(2 x + \frac{\pi}{2} \right)} - \frac{\sin^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - \sin{\left(x + \frac{\pi}{2} \right)}}$$

      1                         1                
------------- - ---------------------------------
   /pi      \   /       1           2   \    2   
csc|-- - 2*x|   |- ----------- + -------|*csc (x)
   \2       /   |     /pi    \      2   |        
                |  csc|-- - x|   csc (x)|        
                \     \2     /          /

$$\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}} - \frac{1}{\left(- \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{2}{\csc^{2}{\left(x \right)}}\right) \csc^{2}{\left(x \right)}}$$

                         1           
                 -1 + --------       
   1                  sec(2*x)       
-------- - --------------------------
sec(2*x)     /       1         1    \
           2*|-1 + ------ + --------|
             \     sec(x)   sec(2*x)/

$$- \frac{-1 + \frac{1}{\sec{\left(2 x \right)}}}{2 \left(-1 + \frac{1}{\sec{\left(2 x \right)}} + \frac{1}{\sec{\left(x \right)}}\right)} + \frac{1}{\sec{\left(2 x \right)}}$$

   1                         1                   
-------- - --------------------------------------
sec(2*x)   /    1           2      \    2/    pi\
           |- ------ + ------------|*sec |x - --|
           |  sec(x)      2/    pi\|     \    2 /
           |           sec |x - --||             
           \               \    2 //

$$\frac{1}{\sec{\left(2 x \right)}} - \frac{1}{\left(\frac{2}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(x \right)}}\right) \sec^{2}{\left(x - \frac{\pi}{2} \right)}}$$

                                    1               
                         -1 + -------------         
                                 /pi      \         
                              csc|-- - 2*x|         
      1                          \2       /         
------------- - ------------------------------------
   /pi      \     /          1              1      \
csc|-- - 2*x|   2*|-1 + ----------- + -------------|
   \2       /     |        /pi    \      /pi      \|
                  |     csc|-- - x|   csc|-- - 2*x||
                  \        \2     /      \2       //

$$- \frac{-1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}}{2 \left(-1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right)} + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}$$

1/csc(pi/2 - 2*x) - (-1 + 1/csc(pi/2 - 2*x))/(2*(-1 + 1/csc(pi/2 - x) + 1/csc(pi/2 - 2*x)))

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¿Cómo vas a descomponer esta cos2x-sin^2/(2sin^2-cosx) expresión en fracciones?

Solución