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¿cómo vas a descomponer esta expresión en fracciones?:
y/(y+3)+y/3+2/y
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))
2*x/(x^2+1)-2*x*(x^2-1)/(x^2+1)^2
(y/(x*y-x^2)+x/(x*y-y^2))/(x^2+2*x*y+y^2)/(1/x+1/y)
Factorizar el polinomio:
z^2+6927*31421
z^2+9*z+27+27/z
z^2+5*i/z
y^2/y-8-64/y-8
Descomponer al cuadrado:
-y^4+7*y^2+7
-y^4-7*y^2+9
-y^4+7*y^2-4
y^4-7*y^2+5
Expresiones idénticas
cos(x-pi/ dos)^(dos)*cot(x+pi/ dos)^(dos)/(cos(x+pi/ dos)+cot(x-pi/ dos)*cot(x-pi/ dos)-cos(x+pi/ dos))
coseno de (x menos número pi dividir por 2) en el grado (2) multiplicar por cotangente de (x más número pi dividir por 2) en el grado (2) dividir por ( coseno de (x más número pi dividir por 2) más cotangente de (x menos número pi dividir por 2) multiplicar por cotangente de (x menos número pi dividir por 2) menos coseno de (x más número pi dividir por 2))
coseno de (x menos número pi dividir por dos) en el grado (dos) multiplicar por cotangente de (x más número pi dividir por dos) en el grado (dos) dividir por ( coseno de (x más número pi dividir por dos) más cotangente de (x menos número pi dividir por dos) multiplicar por cotangente de (x menos número pi dividir por dos) menos coseno de (x más número pi dividir por dos))
cos(x-pi/2)(2)*cot(x+pi/2)(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2))
cosx-pi/22*cotx+pi/22/cosx+pi/2+cotx-pi/2*cotx-pi/2-cosx+pi/2
cos(x-pi/2)^(2)cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)cot(x-pi/2)-cos(x+pi/2))
cos(x-pi/2)(2)cot(x+pi/2)(2)/(cos(x+pi/2)+cot(x-pi/2)cot(x-pi/2)-cos(x+pi/2))
cosx-pi/22cotx+pi/22/cosx+pi/2+cotx-pi/2cotx-pi/2-cosx+pi/2
cosx-pi/2^2cotx+pi/2^2/cosx+pi/2+cotx-pi/2cotx-pi/2-cosx+pi/2
cos(x-pi dividir por 2)^(2)*cot(x+pi dividir por 2)^(2) dividir por (cos(x+pi dividir por 2)+cot(x-pi dividir por 2)*cot(x-pi dividir por 2)-cos(x+pi dividir por 2))
Expresiones semejantes
cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x-pi/2))
cos(x+pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2))
cos(x-pi/2)^(2)*cot(x-pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2))
cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x-pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2))
cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x+pi/2)*cot(x-pi/2)-cos(x+pi/2))
cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)+cos(x+pi/2))
cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x+pi/2)-cos(x+pi/2))
cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)-cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2))
Expresiones con funciones
Coseno cos
cos(3*pi/(2+a))/sin(a)
cos(x)/(cos(x+pi/6))
cos(x)^atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)^2)-atan(x+pi/4)*sin(x)/cos(x))
cos(x)^atan(x)*(log(cos(x))/(1+x^2)-atan(x)*sin(x)/cos(x))
cos(x/2)/(x-n^4)
Coseno cos
cos(3*pi/(2+a))/sin(a)
cos(x)/(cos(x+pi/6))
cos(x)^atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)^2)-atan(x+pi/4)*sin(x)/cos(x))
cos(x)^atan(x)*(log(cos(x))/(1+x^2)-atan(x)*sin(x)/cos(x))
cos(x/2)/(x-n^4)
Coseno cos
cos(3*pi/(2+a))/sin(a)
cos(x)/(cos(x+pi/6))
cos(x)^atan(x+pi/4)*(log(cos(x))/(1+(x+pi/4)^2)-atan(x+pi/4)*sin(x)/cos(x))
cos(x)^atan(x)*(log(cos(x))/(1+x^2)-atan(x)*sin(x)/cos(x))
cos(x/2)/(x-n^4)

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2))

¿Cómo vas a descomponer esta cos(x-pi/2)^(2)cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)cot(x-pi/2)-cos(x+pi/2)) expresión en fracciones?

Solución

Ha introducido [src]

                2/    pi\    2/    pi\             
             cos |x - --|*cot |x + --|             
                 \    2 /     \    2 /             
---------------------------------------------------
   /    pi\      /    pi\    /    pi\      /    pi\
cos|x + --| + cot|x - --|*cot|x - --| - cos|x + --|
   \    2 /      \    2 /    \    2 /      \    2 /

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

(cos(x - pi/2)^2*cot(x + pi/2)^2)/(cos(x + pi/2) + cot(x - pi/2)*cot(x - pi/2) - cos(x + pi/2))

Descomposición de una fracción [src]

sin(x)^2

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

   2   
sin (x)

Simplificación general [src]

   2   
sin (x)

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

sin(x)^2

Respuesta numérica [src]

cos(x - pi/2)^2*cot(x + pi/2)^2/cot(x - pi/2)^2

cos(x - pi/2)^2*cot(x + pi/2)^2/cot(x - pi/2)^2

Denominador común [src]

   2   
sin (x)

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

sin(x)^2

Combinatoria [src]

   2   
sin (x)

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

sin(x)^2

Potencias [src]

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

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

   2   
sin (x)

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

sin(x)^2

Abrimos la expresión [src]

   2   
sin (x)

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

sin(x)^2

Compilar la expresión [src]

   2/    pi\    2/    pi\
cos |x - --|*cot |x + --|
    \    2 /     \    2 /
-------------------------
          2/    pi\      
       cot |x - --|      
           \    2 /

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

cos(x - pi/2)^2*cot(x + pi/2)^2/cot(x - pi/2)^2

Parte trigonométrica [src]

                  2
/       2/x   pi\\ 
|1 - cot |- + --|| 
\        \2   4 // 
-------------------
                  2
/       2/x   pi\\ 
|1 + cot |- + --|| 
\        \2   4 //

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

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

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

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

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

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

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

                                     2
                    /           /x\ \ 
                  2 |      2*cot|-| | 
/       2/x   pi\\  |           \2/ | 
|1 - cot |- + --|| *|1 + -----------| 
\        \2   4 //  |           2/x\| 
                    |    1 + cot |-|| 
                    \            \2// 
--------------------------------------
                  4

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

                                     2
                    /           /x\ \ 
                  2 |      2*tan|-| | 
/         1      \  |           \2/ | 
|1 - ------------| *|1 + -----------| 
|       2/x   pi\|  |           2/x\| 
|    tan |- + --||  |    1 + tan |-|| 
\        \2   4 //  \            \2// 
--------------------------------------
                  4

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

       4              4      
- ------------ + ------------
     4/pi   x\      2/pi   x\
  csc |-- - -|   csc |-- - -|
      \2    2/       \2    2/

$$\frac{4}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - \frac{4}{\csc^{4}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}$$

                  4                   2
    /        2/x\\      /        2/x\\ 
  4*|-1 + cot |-||    4*|-1 + cot |-|| 
    \         \4//      \         \4// 
- ----------------- + -----------------
                 4                   2 
    /       2/x\\       /       2/x\\  
    |1 + cot |-||       |1 + cot |-||  
    \        \4//       \        \4//

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

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

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

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

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

                 4                  2
    /       2/x\\      /       2/x\\ 
  4*|1 - tan |-||    4*|1 - tan |-|| 
    \        \4//      \        \4// 
- ---------------- + ----------------
                4                  2 
   /       2/x\\      /       2/x\\  
   |1 + tan |-||      |1 + tan |-||  
   \        \4//      \        \4//

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

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

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

     4         4   
- ------- + -------
     4/x\      2/x\
  sec |-|   sec |-|
      \2/       \2/

$$\frac{4}{\sec^{2}{\left(\frac{x}{2} \right)}} - \frac{4}{\sec^{4}{\left(\frac{x}{2} \right)}}$$

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

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

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

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

       4/x\        2/x\
- 4*cos |-| + 4*cos |-|
        \2/         \2/

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

                  2
/         1      \ 
|1 - ------------| 
|       2/x   pi\| 
|    tan |- + --|| 
\        \2   4 // 
-------------------
                  2
/         1      \ 
|1 + ------------| 
|       2/x   pi\| 
|    tan |- + --|| 
\        \2   4 //

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

                   2
/        2/x   pi\\ 
|-1 + tan |- + --|| 
\         \2   4 // 
--------------------
                  2 
/       2/x   pi\\  
|1 + tan |- + --||  
\        \2   4 //

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

                  2                   
/       2/x   pi\\                    
|    cos |- + --||                   2
|        \2   4 /|  /       /    pi\\ 
|1 - ------------| *|1 + cos|x - --|| 
|       2/x   pi\|  \       \    2 // 
|    cos |- - --||                    
\        \2   4 //                    
--------------------------------------
                  4

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

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

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

                    2              
/          2       \               
|       cos (x)    |              2
|1 - --------------| *(1 + sin(x)) 
|         4/x   pi\|               
|    4*sin |- + --||               
\          \2   4 //               
-----------------------------------
                 4

$$\frac{\left(1 - \frac{\cos^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}\right)^{2} \left(\sin{\left(x \right)} + 1\right)^{2}}{4}$$

   2   
sin (x)

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

                                  2
              /        2/x   pi\ \ 
            2 |     csc |- + --| | 
/      1   \  |         \2   4 / | 
|1 + ------| *|1 - --------------| 
\    csc(x)/  |       2/  x   pi\| 
              |    csc |- - + --|| 
              \        \  2   4 // 
-----------------------------------
                 4

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

                                     2
                   /       2/x   pi\\ 
                 2 |    sec |- - --|| 
/         1     \  |        \2   4 /| 
|1 + -----------| *|1 - ------------| 
|       /    pi\|  |       2/x   pi\| 
|    sec|x - --||  |    sec |- + --|| 
\       \    2 //  \        \2   4 // 
--------------------------------------
                  4

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

   1   
-------
   2   
csc (x)

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

       4/pi   x\        2/pi   x\
- 4*sin |-- + -| + 4*sin |-- + -|
        \2    2/         \2    2/

$$- 4 \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{2} \right)} + 4 \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}$$

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

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

                   2
/          1      \ 
|-1 + ------------| 
|        2/x   pi\| 
|     cot |- + --|| 
\         \2   4 // 
--------------------
                  2 
/         1      \  
|1 + ------------|  
|       2/x   pi\|  
|    cot |- + --||  
\        \2   4 //

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

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

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

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

Unión de expresiones racionales [src]

   2/-pi + 2*x\    2/pi + 2*x\
cos |---------|*cot |--------|
    \    2    /     \   2    /
------------------------------
          2/-pi + 2*x\        
       cot |---------|        
           \    2    /

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

cos((-pi + 2*x)/2)^2*cot((pi + 2*x)/2)^2/cot((-pi + 2*x)/2)^2

Denominador racional [src]

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

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

cot(x + pi/2)^2*sin(x)^2/tan(x)^2

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta cos(x-pi/2)^(2)*cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)*cot(x-pi/2)-cos(x+pi/2)) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta cos(x-pi/2)^(2)cot(x+pi/2)^(2)/(cos(x+pi/2)+cot(x-pi/2)cot(x-pi/2)-cos(x+pi/2)) expresión en fracciones?