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¿cómo vas a descomponer esta expresión en fracciones?:
(z*(z^2+6*z+1)-(4*z*(z+1)))/(z-1)^3+z*(z-1)/(z+1)^3
(z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)
((x^3+y^3)/(x+y))/(x^2-y^2)+(2*y)/(x+y)-(x*y)/(x^2-y^2)
-(z^2+1)/(z-(-1-sqrt(3)*i)/2)^2+2*z/(z-(-1-sqrt(3)*i)/2)
Factorizar el polinomio:
z^2/2-4*z
z^2+20*z+100
z^2-z+1
z^2-16+64/8-z
Descomponer al cuadrado:
y^4+y^2+2
-y^4+y^2+15
y^4-y^2+11
-y^4+y^2+2
Expresiones idénticas
ctgx*(3tgy+ctgx)/(tgx+3ctgy)
ctgx multiplicar por (3tgy más ctgx) dividir por (tgx más 3ctgy)
ctgx(3tgy+ctgx)/(tgx+3ctgy)
ctgx3tgy+ctgx/tgx+3ctgy
ctgx*(3tgy+ctgx) dividir por (tgx+3ctgy)
Expresiones semejantes
ctgx*(3tgy-ctgx)/(tgx+3ctgy)
ctgx*(3tgy+ctgx)/(tgx-3ctgy)
Expresiones con funciones
tgx
tgx+(cos^3x-sin^3x)/(1+sinx*cosx)*cos^2x
tgx/(1-(tgx)^2)+ctgx/(1+(ctgx)^2)

Simplificación de expresiones/ Descomposición en fracciones simples/ ctgx*(3tgy+ctgx)/(tgx+3ctgy)

¿Cómo vas a descomponer esta ctgx*(3tgy+ctgx)/(tgx+3ctgy) expresión en fracciones?

Solución

Ha introducido [src]

cot(x)*(3*tan(y) + cot(x))
--------------------------
    tan(x) + 3*cot(y)

$$\frac{\left(3 \tan{\left(y \right)} + \cot{\left(x \right)}\right) \cot{\left(x \right)}}{\tan{\left(x \right)} + 3 \cot{\left(y \right)}}$$

(cot(x)*(3*tan(y) + cot(x)))/(tan(x) + 3*cot(y))

Respuesta numérica [src]

(3.0*tan(y) + cot(x))*cot(x)/(3.0*cot(y) + tan(x))

(3.0*tan(y) + cot(x))*cot(x)/(3.0*cot(y) + tan(x))

Denominador común [src]

   2                     
cot (x) + 3*cot(x)*tan(y)
-------------------------
    3*cot(y) + tan(x)

$$\frac{3 \tan{\left(y \right)} \cot{\left(x \right)} + \cot^{2}{\left(x \right)}}{\tan{\left(x \right)} + 3 \cot{\left(y \right)}}$$

(cot(x)^2 + 3*cot(x)*tan(y))/(3*cot(y) + tan(x))

Potencias [src]

/    /   I*y    -I*y\         \       
|3*I*\- e    + e    /         |       
|-------------------- + cot(x)|*cot(x)
|     I*y    -I*y             |       
\    e    + e                 /       
--------------------------------------
                 /   I*x    -I*x\     
               I*\- e    + e    /     
    3*cot(y) + ------------------     
                   I*x    -I*x        
                  e    + e

$$\frac{\left(\frac{3 i \left(- e^{i y} + e^{- i y}\right)}{e^{i y} + e^{- i y}} + \cot{\left(x \right)}\right) \cot{\left(x \right)}}{\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} + 3 \cot{\left(y \right)}}$$

(3*i*(-exp(i*y) + exp(-i*y))/(exp(i*y) + exp(-i*y)) + cot(x))*cot(x)/(3*cot(y) + i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))

Parte trigonométrica [src]

/  3            \       
|------ + cot(x)|*cot(x)
\cot(y)         /       
------------------------
     1                  
   ------ + 3*cot(y)    
   cot(x)

$$\frac{\left(\cot{\left(x \right)} + \frac{3}{\cot{\left(y \right)}}\right) \cot{\left(x \right)}}{3 \cot{\left(y \right)} + \frac{1}{\cot{\left(x \right)}}}$$

     1                  
   ------ + 3*tan(y)    
   tan(x)               
------------------------
/  3            \       
|------ + tan(x)|*tan(x)
\tan(y)         /

$$\frac{3 \tan{\left(y \right)} + \frac{1}{\tan{\left(x \right)}}}{\left(\tan{\left(x \right)} + \frac{3}{\tan{\left(y \right)}}\right) \tan{\left(x \right)}}$$

/  1              \       
|------ + 3*tan(y)|*tan(y)
\tan(x)           /       
--------------------------
(3 + tan(x)*tan(y))*tan(x)

$$\frac{\left(3 \tan{\left(y \right)} + \frac{1}{\tan{\left(x \right)}}\right) \tan{\left(y \right)}}{\left(\tan{\left(x \right)} \tan{\left(y \right)} + 3\right) \tan{\left(x \right)}}$$

/   /    pi\              \            
|sec|x - --|              |            
|   \    2 /     3*sec(y) |    /    pi\
|----------- + -----------|*sec|x - --|
|   sec(x)        /    pi\|    \    2 /
|              sec|y - --||            
\                 \    2 //            
---------------------------------------
  /                   /    pi\\        
  |              3*sec|y - --||        
  |   sec(x)          \    2 /|        
  |----------- + -------------|*sec(x) 
  |   /    pi\       sec(y)   |        
  |sec|x - --|                |        
  \   \    2 /                /

$$\frac{\left(\frac{3 \sec{\left(y \right)}}{\sec{\left(y - \frac{\pi}{2} \right)}} + \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{3 \sec{\left(y - \frac{\pi}{2} \right)}}{\sec{\left(y \right)}}\right) \sec{\left(x \right)}}$$

/        2/x\\ /  3            \
|-1 + cot |-||*|------ + cot(x)|
\         \2// \cot(y)         /
--------------------------------
    /  1              \    /x\  
  2*|------ + 3*cot(y)|*cot|-|  
    \cot(x)           /    \2/

$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\cot{\left(x \right)} + \frac{3}{\cot{\left(y \right)}}\right)}{2 \left(3 \cot{\left(y \right)} + \frac{1}{\cot{\left(x \right)}}\right) \cot{\left(\frac{x}{2} \right)}}$$

        /                 2   \         
   2    | sin(2*x)   6*sin (y)|         
sin (y)*|--------- + ---------|*sin(2*x)
        |     2       sin(2*y)|         
        \2*sin (x)            /         
----------------------------------------
/         2       2   \                 
|    4*sin (x)*sin (y)|    2            
|3 + -----------------|*sin (x)*sin(2*y)
\    sin(2*x)*sin(2*y)/

$$\frac{\left(\frac{6 \sin^{2}{\left(y \right)}}{\sin{\left(2 y \right)}} + \frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}\right) \sin{\left(2 x \right)} \sin^{2}{\left(y \right)}}{\left(\frac{4 \sin^{2}{\left(x \right)} \sin^{2}{\left(y \right)}}{\sin{\left(2 x \right)} \sin{\left(2 y \right)}} + 3\right) \sin^{2}{\left(x \right)} \sin{\left(2 y \right)}}$$

 /                 2   \          
 | sin(2*x)   6*sin (y)|          
 |--------- + ---------|*sin(2*x) 
 |     2       sin(2*y)|          
 \2*sin (x)            /          
----------------------------------
  /     2                \        
  |2*sin (x)   3*sin(2*y)|    2   
2*|--------- + ----------|*sin (x)
  | sin(2*x)        2    |        
  \            2*sin (y) /

$$\frac{\left(\frac{6 \sin^{2}{\left(y \right)}}{\sin{\left(2 y \right)}} + \frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}\right) \sin{\left(2 x \right)}}{2 \left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + \frac{3 \sin{\left(2 y \right)}}{2 \sin^{2}{\left(y \right)}}\right) \sin^{2}{\left(x \right)}}$$

(3*tan(y) + cot(x))*cot(x)*tan(y)
---------------------------------
        3 + tan(x)*tan(y)

$$\frac{\left(3 \tan{\left(y \right)} + \cot{\left(x \right)}\right) \tan{\left(y \right)} \cot{\left(x \right)}}{\tan{\left(x \right)} \tan{\left(y \right)} + 3}$$

 /  3            \        
 |------ + cot(x)|*cot(x) 
 \cot(y)         /        
--------------------------
/          1      \       
|3 + -------------|*cot(y)
\    cot(x)*cot(y)/

$$\frac{\left(\cot{\left(x \right)} + \frac{3}{\cot{\left(y \right)}}\right) \cot{\left(x \right)}}{\left(3 + \frac{1}{\cot{\left(x \right)} \cot{\left(y \right)}}\right) \cot{\left(y \right)}}$$

/   /    pi\              \            
|sec|x - --|              |            
|   \    2 /     3*sec(y) |    /pi    \
|----------- + -----------|*sec|-- - x|
|   sec(x)        /    pi\|    \2     /
|              sec|y - --||            
\                 \    2 //            
---------------------------------------
  /                   /    pi\\        
  |              3*sec|y - --||        
  |   sec(x)          \    2 /|        
  |----------- + -------------|*sec(x) 
  |   /    pi\       sec(y)   |        
  |sec|x - --|                |        
  \   \    2 /                /

$$\frac{\left(\frac{3 \sec{\left(y \right)}}{\sec{\left(y - \frac{\pi}{2} \right)}} + \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right) \sec{\left(- x + \frac{\pi}{2} \right)}}{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{3 \sec{\left(y - \frac{\pi}{2} \right)}}{\sec{\left(y \right)}}\right) \sec{\left(x \right)}}$$

  /                   /pi    \\        
  |              3*csc|-- - y||        
  |   csc(x)          \2     /|        
  |----------- + -------------|*csc(x) 
  |   /pi    \       csc(y)   |        
  |csc|-- - x|                |        
  \   \2     /                /        
---------------------------------------
/   /pi    \              \            
|csc|-- - x|              |            
|   \2     /     3*csc(y) |    /pi    \
|----------- + -----------|*csc|-- - x|
|   csc(x)        /pi    \|    \2     /
|              csc|-- - y||            
\                 \2     //

$$\frac{\left(\frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{3 \csc{\left(- y + \frac{\pi}{2} \right)}}{\csc{\left(y \right)}}\right) \csc{\left(x \right)}}{\left(\frac{3 \csc{\left(y \right)}}{\csc{\left(- y + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right) \csc{\left(- x + \frac{\pi}{2} \right)}}$$

/  1              \              
|------ + 3*tan(y)|*cos(x)*csc(x)
\tan(x)           /              
---------------------------------
           3                     
         ------ + tan(x)         
         tan(y)

$$\frac{\left(3 \tan{\left(y \right)} + \frac{1}{\tan{\left(x \right)}}\right) \cos{\left(x \right)} \csc{\left(x \right)}}{\tan{\left(x \right)} + \frac{3}{\tan{\left(y \right)}}}$$

  /                   /    pi\\        
  |              3*cos|y - --||        
  |   cos(x)          \    2 /|        
  |----------- + -------------|*cos(x) 
  |   /    pi\       cos(y)   |        
  |cos|x - --|                |        
  \   \    2 /                /        
---------------------------------------
/   /    pi\              \            
|cos|x - --|              |            
|   \    2 /     3*cos(y) |    /    pi\
|----------- + -----------|*cos|x - --|
|   cos(x)        /    pi\|    \    2 /
|              cos|y - --||            
\                 \    2 //

$$\frac{\left(\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{3 \cos{\left(y - \frac{\pi}{2} \right)}}{\cos{\left(y \right)}}\right) \cos{\left(x \right)}}{\left(\frac{3 \cos{\left(y \right)}}{\cos{\left(y - \frac{\pi}{2} \right)}} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right) \cos{\left(x - \frac{\pi}{2} \right)}}$$

 /   /    pi\              \                    
 |sec|x - --|              |                    
 |   \    2 /     3*sec(y) |           /    pi\ 
 |----------- + -----------|*sec(y)*sec|x - --| 
 |   sec(x)        /    pi\|           \    2 / 
 |              sec|y - --||                    
 \                 \    2 //                    
------------------------------------------------
/         sec(x)*sec(y)     \           /    pi\
|3 + -----------------------|*sec(x)*sec|y - --|
|       /    pi\    /    pi\|           \    2 /
|    sec|x - --|*sec|y - --||                   
\       \    2 /    \    2 //

$$\frac{\left(\frac{3 \sec{\left(y \right)}}{\sec{\left(y - \frac{\pi}{2} \right)}} + \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right) \sec{\left(y \right)} \sec{\left(x - \frac{\pi}{2} \right)}}{\left(\frac{\sec{\left(x \right)} \sec{\left(y \right)}}{\sec{\left(x - \frac{\pi}{2} \right)} \sec{\left(y - \frac{\pi}{2} \right)}} + 3\right) \sec{\left(x \right)} \sec{\left(y - \frac{\pi}{2} \right)}}$$

/        2/x\\                        /x\
|-1 + cot |-||*(3*tan(y) + cot(x))*tan|-|
\         \2//                        \2/
-----------------------------------------
          2*(3*cot(y) + tan(x))

$$\frac{\left(3 \tan{\left(y \right)} + \cot{\left(x \right)}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \tan{\left(\frac{x}{2} \right)}}{2 \left(\tan{\left(x \right)} + 3 \cot{\left(y \right)}\right)}$$

/csc(x)   3*sec(y)\       
|------ + --------|*csc(x)
\sec(x)    csc(y) /       
--------------------------
/sec(x)   3*csc(y)\       
|------ + --------|*sec(x)
\csc(x)    sec(y) /

$$\frac{\left(\frac{\csc{\left(x \right)}}{\sec{\left(x \right)}} + \frac{3 \sec{\left(y \right)}}{\csc{\left(y \right)}}\right) \csc{\left(x \right)}}{\left(\frac{3 \csc{\left(y \right)}}{\sec{\left(y \right)}} + \frac{\sec{\left(x \right)}}{\csc{\left(x \right)}}\right) \sec{\left(x \right)}}$$

/cos(x)   3*sin(y)\       
|------ + --------|*cos(x)
\sin(x)    cos(y) /       
--------------------------
/sin(x)   3*cos(y)\       
|------ + --------|*sin(x)
\cos(x)    sin(y) /

$$\frac{\left(\frac{3 \sin{\left(y \right)}}{\cos{\left(y \right)}} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{3 \cos{\left(y \right)}}{\sin{\left(y \right)}}\right) \sin{\left(x \right)}}$$

/                 2   \            
| sin(2*x)   6*sin (y)|    /    pi\
|--------- + ---------|*sin|x + --|
|     2       sin(2*y)|    \    2 /
\2*sin (x)            /            
-----------------------------------
  /     2                \         
  |2*sin (x)   3*sin(2*y)|         
  |--------- + ----------|*sin(x)  
  | sin(2*x)        2    |         
  \            2*sin (y) /

$$\frac{\left(\frac{6 \sin^{2}{\left(y \right)}}{\sin{\left(2 y \right)}} + \frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}\right) \sin{\left(x + \frac{\pi}{2} \right)}}{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + \frac{3 \sin{\left(2 y \right)}}{2 \sin^{2}{\left(y \right)}}\right) \sin{\left(x \right)}}$$

/       2/x\\ /  1              \
|1 - tan |-||*|------ + 3*tan(y)|
\        \2// \tan(x)           /
---------------------------------
      /  3            \    /x\   
    2*|------ + tan(x)|*tan|-|   
      \tan(y)         /    \2/

$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(3 \tan{\left(y \right)} + \frac{1}{\tan{\left(x \right)}}\right)}{2 \left(\tan{\left(x \right)} + \frac{3}{\tan{\left(y \right)}}\right) \tan{\left(\frac{x}{2} \right)}}$$

/                   /pi    \\                   
|              3*csc|-- - y||                   
|   csc(x)          \2     /|           /pi    \
|----------- + -------------|*csc(x)*csc|-- - y|
|   /pi    \       csc(y)   |           \2     /
|csc|-- - x|                |                   
\   \2     /                /                   
------------------------------------------------
/       /pi    \    /pi    \\                   
|    csc|-- - x|*csc|-- - y||                   
|       \2     /    \2     /|           /pi    \
|3 + -----------------------|*csc(y)*csc|-- - x|
\         csc(x)*csc(y)     /           \2     /

$$\frac{\left(\frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{3 \csc{\left(- y + \frac{\pi}{2} \right)}}{\csc{\left(y \right)}}\right) \csc{\left(x \right)} \csc{\left(- y + \frac{\pi}{2} \right)}}{\left(3 + \frac{\csc{\left(- x + \frac{\pi}{2} \right)} \csc{\left(- y + \frac{\pi}{2} \right)}}{\csc{\left(x \right)} \csc{\left(y \right)}}\right) \csc{\left(y \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}$$

/                   /    pi\\                   
|              3*cos|y - --||                   
|   cos(x)          \    2 /|           /    pi\
|----------- + -------------|*cos(x)*cos|y - --|
|   /    pi\       cos(y)   |           \    2 /
|cos|x - --|                |                   
\   \    2 /                /                   
------------------------------------------------
/       /    pi\    /    pi\\                   
|    cos|x - --|*cos|y - --||                   
|       \    2 /    \    2 /|           /    pi\
|3 + -----------------------|*cos(y)*cos|x - --|
\         cos(x)*cos(y)     /           \    2 /

$$\frac{\left(\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{3 \cos{\left(y - \frac{\pi}{2} \right)}}{\cos{\left(y \right)}}\right) \cos{\left(x \right)} \cos{\left(y - \frac{\pi}{2} \right)}}{\left(3 + \frac{\cos{\left(x - \frac{\pi}{2} \right)} \cos{\left(y - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} \cos{\left(y \right)}}\right) \cos{\left(y \right)} \cos{\left(x - \frac{\pi}{2} \right)}}$$

(cos(x)/cos(x - pi/2) + 3*cos(y - pi/2)/cos(y))*cos(x)*cos(y - pi/2)/((3 + cos(x - pi/2)*cos(y - pi/2)/(cos(x)*cos(y)))*cos(y)*cos(x - pi/2))

Abrimos la expresión [src]

        2                            
     cot (x)         3*cot(x)*tan(y) 
----------------- + -----------------
tan(x) + 3*cot(y)   tan(x) + 3*cot(y)

$$\frac{3 \tan{\left(y \right)} \cot{\left(x \right)}}{\tan{\left(x \right)} + 3 \cot{\left(y \right)}} + \frac{\cot^{2}{\left(x \right)}}{\tan{\left(x \right)} + 3 \cot{\left(y \right)}}$$

cot(x)^2/(tan(x) + 3*cot(y)) + 3*cot(x)*tan(y)/(tan(x) + 3*cot(y))

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta ctgx*(3tgy+ctgx)/(tgx+3ctgy) expresión en fracciones?

Solución