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¿cómo vas a descomponer esta expresión en fracciones?:
-((-1+x^2/(1+x^2))/sqrt(1+x^2)+(1+x/sqrt(1+x^2))^2/(x+sqrt(1+x^2)))/(x+sqrt(1+x^2))
((z-1)*((z*f*r*f)/(1+(z-1)*c*f)))/(z*r)
(x^2+3*x-4)/(x+4)
y+y/x-y+1/(x^2)-x
Factorizar el polinomio:
y^8-x^8
y-5*x^2/4-11/2
y^4-81
y^5-32
Descomponer al cuadrado:
-y^4+y^2-10
y^4+9*y^2-3
y^4-9*y^2+4
y^4-9*y^2-10
Expresiones idénticas
cos(x)/(uno +cos(x))+sin(x)^ dos /(uno +cos(x))^ dos
coseno de (x) dividir por (1 más coseno de (x)) más seno de (x) al cuadrado dividir por (1 más coseno de (x)) al cuadrado
coseno de (x) dividir por (uno más coseno de (x)) más seno de (x) en el grado dos dividir por (uno más coseno de (x)) en el grado dos
cos(x)/(1+cos(x))+sin(x)2/(1+cos(x))2
cosx/1+cosx+sinx2/1+cosx2
cos(x)/(1+cos(x))+sin(x)²/(1+cos(x))²
cos(x)/(1+cos(x))+sin(x) en el grado 2/(1+cos(x)) en el grado 2
cosx/1+cosx+sinx^2/1+cosx^2
cos(x) dividir por (1+cos(x))+sin(x)^2 dividir por (1+cos(x))^2
Expresiones semejantes
cos(x)/(1+cos(x))-sin(x)^2/(1+cos(x))^2
cos(x)/(1-cos(x))+sin(x)^2/(1+cos(x))^2
cos(x)/(1+cos(x))+sin(x)^2/(1-cos(x))^2
cosx/(1+cosx)+sinx^2/(1+cosx)^2
Expresiones con funciones
Coseno cos
cos(2*t)*t/(cos(t)+sin(t))-cos(t)
cos(b)/(cos*b/2)-(sin*b/2)
cos(x)*log(atan(sqrt(sin(x))))/((1+sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
cos(2*x)/(1-sin(2*x))-(1+tan(x))/(1-tan(x))
cos(2*a)/((cos(a)*cos(a)))
Coseno cos
cos(2*t)*t/(cos(t)+sin(t))-cos(t)
cos(b)/(cos*b/2)-(sin*b/2)
cos(x)*log(atan(sqrt(sin(x))))/((1+sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
cos(2*x)/(1-sin(2*x))-(1+tan(x))/(1-tan(x))
cos(2*a)/((cos(a)*cos(a)))
Seno sin
sin(3*pi/2+a)/(3*cos(pi-a))еслиa=2*pi/3
sin(2*a)/((2*tg(a)))
sin/(a*x-1)-1/(a*x+1)
sin(a+b)*b/((cos(a)*cos(b)))+tan(b)
sin(2*x)/((11*sin(x)))
Coseno cos
cos(2*t)*t/(cos(t)+sin(t))-cos(t)
cos(b)/(cos*b/2)-(sin*b/2)
cos(x)*log(atan(sqrt(sin(x))))/((1+sin(x))*atan(sqrt(sin(x)))*sqrt(sin(x)))
cos(2*x)/(1-sin(2*x))-(1+tan(x))/(1-tan(x))
cos(2*a)/((cos(a)*cos(a)))

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

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

Solución

Ha introducido [src]

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

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

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

Simplificación general [src]

    1     
----------
1 + cos(x)

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

1/(1 + cos(x))

Denominador común [src]

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

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

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

Combinatoria [src]

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

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

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

Potencias [src]

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

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

   I*x    -I*x                          
  e      e                           2  
  ---- + -----       /   -I*x    I*x\   
   2       2         \- e     + e   /   
---------------- - ---------------------
     I*x    -I*x                       2
    e      e         /     I*x    -I*x\ 
1 + ---- + -----     |    e      e    | 
     2       2     4*|1 + ---- + -----| 
                     \     2       2  /

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

(exp(i*x)/2 + exp(-i*x)/2)/(1 + exp(i*x)/2 + exp(-i*x)/2) - (-exp(-i*x) + exp(i*x))^2/(4*(1 + exp(i*x)/2 + exp(-i*x)/2)^2)

Unión de expresiones racionales [src]

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

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

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

Denominador racional [src]

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

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

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

Abrimos la expresión [src]

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

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

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

Compilar la expresión [src]

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

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

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

Parte trigonométrica [src]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    1     
----------
      1   
1 + ------
    sec(x)

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

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

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

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

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

    1     
----------
1 + cos(x)

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

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

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

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

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

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

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

1/(1 + sin(x + pi/2))

Respuesta numérica [src]

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

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

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

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

Solución