Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
¿cómo vas a descomponer esta expresión en fracciones?:
-2*sqrt(3)/(3*sqrt(1-(2*x-1)^2/3))
(x^2-5*x+6)/(x-3)
a^5*b^4/(a*b^3)^2
(2x+3)/(x^2-9)
Factorizar el polinomio:
z^2-36
z^3-2*z^2+z-2
z^2-20*z+104
z^3/4-2*z^3/9+7*z^3/12
Descomponer al cuadrado:
-y^4+y^2+15
-y^4+y^2+11
y^4-9*y^2+7
y^4+9*y^2+8
Expresiones idénticas
cos(x)^ dos /(uno -sin(x))^ dos -sin(x)/(uno -sin(x))
coseno de (x) al cuadrado dividir por (1 menos seno de (x)) al cuadrado menos seno de (x) dividir por (1 menos seno de (x))
coseno de (x) en el grado dos dividir por (uno menos seno de (x)) en el grado dos menos seno de (x) dividir por (uno menos seno de (x))
cos(x)2/(1-sin(x))2-sin(x)/(1-sin(x))
cosx2/1-sinx2-sinx/1-sinx
cos(x)²/(1-sin(x))²-sin(x)/(1-sin(x))
cos(x) en el grado 2/(1-sin(x)) en el grado 2-sin(x)/(1-sin(x))
cosx^2/1-sinx^2-sinx/1-sinx
cos(x)^2 dividir por (1-sin(x))^2-sin(x) dividir por (1-sin(x))
Expresiones semejantes
cos(x)^2/(1-sin(x))^2-sin(x)/(1+sin(x))
cos(x)^2/(1-sin(x))^2+sin(x)/(1-sin(x))
cos(x)^2/(1+sin(x))^2-sin(x)/(1-sin(x))
cosx^2/(1-sinx)^2-sinx/(1-sinx)
Expresiones con funciones
Coseno cos
cos(4*x)/(cos(2*x)-sin(2*x))
cos(x)^5+cos(x)^7/(6*sin(x)^2)
cos(x^2+1)*exp(x)/(1+exp(2*x))-2*x*atan(E^x)*sin(x^2+1)
cos(x)*sin(x)/(cos(x)+sin(x))/(1-cos(x)*sin(x))
cos(sqrt(x))/(2*sqrt(x)*sin(sqrt(x)))
Seno sin
sin(2*x)/((9*sin(x)))
sin(2*x)/((5*sin(x)))
sin(pi+a)+cos(pi+a)/cos(pi/2-a)-sin(3pi/2-a)1/(a*x-1)-1/(a*x+1)
sin(2*x)/((19*sin(x)))
sin10/(2*cos5)
Seno sin
sin(2*x)/((9*sin(x)))
sin(2*x)/((5*sin(x)))
sin(pi+a)+cos(pi+a)/cos(pi/2-a)-sin(3pi/2-a)1/(a*x-1)-1/(a*x+1)
sin(2*x)/((19*sin(x)))
sin10/(2*cos5)
Seno sin
sin(2*x)/((9*sin(x)))
sin(2*x)/((5*sin(x)))
sin(pi+a)+cos(pi+a)/cos(pi/2-a)-sin(3pi/2-a)1/(a*x-1)-1/(a*x+1)
sin(2*x)/((19*sin(x)))
sin10/(2*cos5)

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)^2/(1-sin(x))^2-sin(x)/(1-sin(x))

¿Cómo vas a descomponer esta cos(x)^2/(1-sin(x))^2-sin(x)/(1-sin(x)) expresión en fracciones?

Solución

Ha introducido [src]

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

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

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

Simplificación general [src]

    -1     
-----------
-1 + sin(x)

- \frac{1}{\sin{\left(x \right)} - 1}

-1/(-1 + sin(x))

Respuesta numérica [src]

cos(x)^2/(1.0 - sin(x))^2 - sin(x)/(1.0 - sin(x))

cos(x)^2/(1.0 - sin(x))^2 - sin(x)/(1.0 - sin(x))

Denominador racional [src]

   2                               2       
cos (x)*(1 - sin(x)) - (1 - sin(x)) *sin(x)
-------------------------------------------
                           3               
               (1 - sin(x))

\frac{- \left(1 - \sin{\left(x \right)}\right)^{2} \sin{\left(x \right)} + \left(1 - \sin{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{\left(1 - \sin{\left(x \right)}\right)^{3}}

(cos(x)^2*(1 - sin(x)) - (1 - sin(x))^2*sin(x))/(1 - sin(x))^3

Denominador común [src]

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

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

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

Combinatoria [src]

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

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

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

Abrimos la expresión [src]

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

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

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

Potencias [src]

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

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

                   2                                  
     / I*x    -I*x\                                   
     |e      e    |                                   
     |---- + -----|               /   -I*x    I*x\    
     \ 2       2  /             I*\- e     + e   /    
------------------------- + --------------------------
                        2     /      /   -I*x    I*x\\
/      /   -I*x    I*x\\      |    I*\- e     + e   /|
|    I*\- e     + e   /|    2*|1 + ------------------|
|1 + ------------------|      \            2         /
\            2         /

\frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1\right)} + \frac{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{\left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1\right)^{2}}

(exp(i*x)/2 + exp(-i*x)/2)^2/(1 + i*(-exp(-i*x) + exp(i*x))/2)^2 + i*(-exp(-i*x) + exp(i*x))/(2*(1 + i*(-exp(-i*x) + exp(i*x))/2))

Compilar la expresión [src]

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

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

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

Parte trigonométrica [src]

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

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

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

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

    -1     
-----------
-1 + sin(x)

- \frac{1}{\sin{\left(x \right)} - 1}

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

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

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

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

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

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

    -1     
-----------
       1   
-1 + ------
     csc(x)

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

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

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

                          /    pi\  
        2              cos|x - --|  
     cos (x)              \    2 /  
------------------ - ---------------
                 2          /    pi\
/       /    pi\\    1 - cos|x - --|
|1 - cos|x - --||           \    2 /
\       \    2 //

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

      -1        
----------------
        /    pi\
-1 + cos|x - --|
        \    2 /

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

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

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

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

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

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

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

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

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

    2/    pi\             
 sin |x + --|             
     \    2 /     sin(x)  
------------- - ----------
            2   1 - sin(x)
(1 - sin(x))

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

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

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

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

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

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

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

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

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

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

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

      -1        
----------------
          1     
-1 + -----------
        /    pi\
     sec|x - --|
        \    2 /

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

-1/(-1 + 1/sec(x - pi/2))

Unión de expresiones racionales [src]

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

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

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

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta cos(x)^2/(1-sin(x))^2-sin(x)/(1-sin(x)) expresión en fracciones?

Solución