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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))
(z+1)/(z+2)^3/(z-1)
y/(x-y)+x^2+y^2/(2*x*y-2*x^2)
Factorizar el polinomio:
y^3-2*y^2*z-4*y*z+8*z^2
y^3+2*y^2*x^2-2*x^2
z^2+6927*31421
z^2+9*z+27+27/z
Descomponer al cuadrado:
-y^4+8*y^2+2
y^4+8*y^2-3
-y^4+8*y^2+14
y^4+8*y^2+2
Expresiones idénticas
tg4x/(uno +tg4x*tg3x)
tg4x dividir por (1 más tg4x multiplicar por tg3x)
tg4x dividir por (uno más tg4x multiplicar por tg3x)
tg4x/(1+tg4xtg3x)
tg4x/1+tg4xtg3x
tg4x dividir por (1+tg4x*tg3x)
Expresiones semejantes
tg4x/(1-tg4x*tg3x)

Simplificación de expresiones/ Descomposición en fracciones simples/ tg4x/(1+tg4x*tg3x)

¿Cómo vas a descomponer esta tg4x/(1+tg4x*tg3x) expresión en fracciones?

Solución

Ha introducido [src]

       tan(4*x)      
---------------------
1 + tan(4*x)*tan(3*x)

$$\frac{\tan{\left(4 x \right)}}{\tan{\left(3 x \right)} \tan{\left(4 x \right)} + 1}$$

tan(4*x)/(1 + tan(4*x)*tan(3*x))

Respuesta numérica [src]

tan(4*x)/(1.0 + tan(3*x)*tan(4*x))

tan(4*x)/(1.0 + tan(3*x)*tan(4*x))

Potencias [src]

                        /   4*I*x    -4*I*x\                      
                      I*\- e      + e      /                      
------------------------------------------------------------------
/    /   3*I*x    -3*I*x\ /   4*I*x    -4*I*x\\                   
|    \- e      + e      /*\- e      + e      /| / -4*I*x    4*I*x\
|1 - -----------------------------------------|*\e       + e     /
|      / -4*I*x    4*I*x\ / -3*I*x    3*I*x\  |                   
\      \e       + e     /*\e       + e     /  /

$$\frac{i \left(- e^{4 i x} + e^{- 4 i x}\right)}{\left(- \frac{\left(- e^{3 i x} + e^{- 3 i x}\right) \left(- e^{4 i x} + e^{- 4 i x}\right)}{\left(e^{3 i x} + e^{- 3 i x}\right) \left(e^{4 i x} + e^{- 4 i x}\right)} + 1\right) \left(e^{4 i x} + e^{- 4 i x}\right)}$$

i*(-exp(4*i*x) + exp(-4*i*x))/((1 - (-exp(3*i*x) + exp(-3*i*x))*(-exp(4*i*x) + exp(-4*i*x))/((exp(-4*i*x) + exp(4*i*x))*(exp(-3*i*x) + exp(3*i*x))))*(exp(-4*i*x) + exp(4*i*x)))

Abrimos la expresión [src]

                                                                                                                    3                                                                                                                                                                                                                                                                                                                                                        
                                                                                                               4*tan (x)                                                                                                                                                                                                                               4*tan(x)                                                                                                              
- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                4                                        8                                       10                                        2                                        6                                                                  4                                        8                                       10                                        2                                        6                 
         4           2                    88*tan (x)                               40*tan (x)                               4*tan  (x)                               12*tan (x)                              112*tan (x)                        4           2                    88*tan (x)                               40*tan (x)                               4*tan  (x)                               12*tan (x)                              112*tan (x)              
  1 + tan (x) - 6*tan (x) - -------------------------------------- - -------------------------------------- + -------------------------------------- + -------------------------------------- + --------------------------------------   1 + tan (x) - 6*tan (x) - -------------------------------------- - -------------------------------------- + -------------------------------------- + -------------------------------------- + --------------------------------------
                                     2           6            4               2           6            4               2           6            4               2           6            4               2           6            4                                         2           6            4               2           6            4               2           6            4               2           6            4               2           6            4   
                            1 - 9*tan (x) - 3*tan (x) + 19*tan (x)   1 - 9*tan (x) - 3*tan (x) + 19*tan (x)   1 - 9*tan (x) - 3*tan (x) + 19*tan (x)   1 - 9*tan (x) - 3*tan (x) + 19*tan (x)   1 - 9*tan (x) - 3*tan (x) + 19*tan (x)                             1 - 9*tan (x) - 3*tan (x) + 19*tan (x)   1 - 9*tan (x) - 3*tan (x) + 19*tan (x)   1 - 9*tan (x) - 3*tan (x) + 19*tan (x)   1 - 9*tan (x) - 3*tan (x) + 19*tan (x)   1 - 9*tan (x) - 3*tan (x) + 19*tan (x)

$$- \frac{4 \tan^{3}{\left(x \right)}}{\tan^{4}{\left(x \right)} - 6 \tan^{2}{\left(x \right)} + 1 + \frac{4 \tan^{10}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1} - \frac{40 \tan^{8}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1} + \frac{112 \tan^{6}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1} - \frac{88 \tan^{4}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1} + \frac{12 \tan^{2}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1}} + \frac{4 \tan{\left(x \right)}}{\tan^{4}{\left(x \right)} - 6 \tan^{2}{\left(x \right)} + 1 + \frac{4 \tan^{10}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1} - \frac{40 \tan^{8}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1} + \frac{112 \tan^{6}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1} - \frac{88 \tan^{4}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1} + \frac{12 \tan^{2}{\left(x \right)}}{- 3 \tan^{6}{\left(x \right)} + 19 \tan^{4}{\left(x \right)} - 9 \tan^{2}{\left(x \right)} + 1}}$$

-4*tan(x)^3/(1 + tan(x)^4 - 6*tan(x)^2 - 88*tan(x)^4/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4) - 40*tan(x)^8/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4) + 4*tan(x)^10/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4) + 12*tan(x)^2/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4) + 112*tan(x)^6/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4)) + 4*tan(x)/(1 + tan(x)^4 - 6*tan(x)^2 - 88*tan(x)^4/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4) - 40*tan(x)^8/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4) + 4*tan(x)^10/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4) + 12*tan(x)^2/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4) + 112*tan(x)^6/(1 - 9*tan(x)^2 - 3*tan(x)^6 + 19*tan(x)^4))

Parte trigonométrica [src]

             2*csc(8*x)            
-----------------------------------
/    4*csc(6*x)*csc(8*x)\    2     
|1 + -------------------|*csc (4*x)
|       2         2     |          
\    csc (3*x)*csc (4*x)/

$$\frac{2 \csc{\left(8 x \right)}}{\left(1 + \frac{4 \csc{\left(6 x \right)} \csc{\left(8 x \right)}}{\csc^{2}{\left(3 x \right)} \csc^{2}{\left(4 x \right)}}\right) \csc^{2}{\left(4 x \right)}}$$

               2*tan(2*x)              
---------------------------------------
/       2     \                        
\1 - tan (2*x)/*(1 + tan(3*x)*tan(4*x))

$$\frac{2 \tan{\left(2 x \right)}}{\left(1 - \tan^{2}{\left(2 x \right)}\right) \left(\tan{\left(3 x \right)} \tan{\left(4 x \right)} + 1\right)}$$

                 sin(4*x)                
-----------------------------------------
/         2         2     \              
|    4*sin (3*x)*sin (4*x)|    /pi      \
|1 + ---------------------|*sin|-- + 4*x|
\      sin(6*x)*sin(8*x)  /    \2       /

$$\frac{\sin{\left(4 x \right)}}{\left(\frac{4 \sin^{2}{\left(3 x \right)} \sin^{2}{\left(4 x \right)}}{\sin{\left(6 x \right)} \sin{\left(8 x \right)}} + 1\right) \sin{\left(4 x + \frac{\pi}{2} \right)}}$$

                    2                     
               2*sin (4*x)                
------------------------------------------
/         2         2      \              
|    4*sin (3*x)*sin (4*x) |    /      pi\
|1 + ----------------------|*cos|8*x - --|
|       /      pi\         |    \      2 /
|    cos|8*x - --|*sin(6*x)|              
\       \      2 /         /

$$\frac{2 \sin^{2}{\left(4 x \right)}}{\left(\frac{4 \sin^{2}{\left(3 x \right)} \sin^{2}{\left(4 x \right)}}{\sin{\left(6 x \right)} \cos{\left(8 x - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(8 x - \frac{\pi}{2} \right)}}$$

               2*cot(2*x)               
----------------------------------------
/            1        \ /        2     \
|1 + -----------------|*\-1 + cot (2*x)/
\    cot(3*x)*cot(4*x)/

$$\frac{2 \cot{\left(2 x \right)}}{\left(1 + \frac{1}{\cot{\left(3 x \right)} \cot{\left(4 x \right)}}\right) \left(\cot^{2}{\left(2 x \right)} - 1\right)}$$

   /pi      \         
csc|-- - 4*x|*sin(4*x)
   \2       /         
----------------------
1 + tan(3*x)*tan(4*x)

$$\frac{\sin{\left(4 x \right)} \csc{\left(- 4 x + \frac{\pi}{2} \right)}}{\tan{\left(3 x \right)} \tan{\left(4 x \right)} + 1}$$

            sec(4*x)            
--------------------------------
/    sec(3*x)*sec(4*x)\         
|1 + -----------------|*csc(4*x)
\    csc(3*x)*csc(4*x)/

$$\frac{\sec{\left(4 x \right)}}{\left(1 + \frac{\sec{\left(3 x \right)} \sec{\left(4 x \right)}}{\csc{\left(3 x \right)} \csc{\left(4 x \right)}}\right) \csc{\left(4 x \right)}}$$

            /       2/      pi\\                     
            |1 + tan |2*x + --||*cot(2*x)            
            \        \      4 //                     
-----------------------------------------------------
/       2     \ /            1        \    /      pi\
\1 + cot (2*x)/*|1 + -----------------|*tan|2*x + --|
                \    cot(3*x)*cot(4*x)/    \      4 /

$$\frac{\left(\tan^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right) \cot{\left(2 x \right)}}{\left(1 + \frac{1}{\cot{\left(3 x \right)} \cot{\left(4 x \right)}}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x + \frac{\pi}{4} \right)}}$$

                 2                  
            2*sin (4*x)             
------------------------------------
/         2         2     \         
|    4*sin (3*x)*sin (4*x)|         
|1 + ---------------------|*sin(8*x)
\      sin(6*x)*sin(8*x)  /

$$\frac{2 \sin^{2}{\left(4 x \right)}}{\left(\frac{4 \sin^{2}{\left(3 x \right)} \sin^{2}{\left(4 x \right)}}{\sin{\left(6 x \right)} \sin{\left(8 x \right)}} + 1\right) \sin{\left(8 x \right)}}$$

                 /pi      \               
              csc|-- - 4*x|               
                 \2       /               
------------------------------------------
/       /pi      \    /pi      \\         
|    csc|-- - 4*x|*csc|-- - 3*x||         
|       \2       /    \2       /|         
|1 + ---------------------------|*csc(4*x)
\         csc(3*x)*csc(4*x)     /

$$\frac{\csc{\left(- 4 x + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc{\left(- 4 x + \frac{\pi}{2} \right)} \csc{\left(- 3 x + \frac{\pi}{2} \right)}}{\csc{\left(3 x \right)} \csc{\left(4 x \right)}}\right) \csc{\left(4 x \right)}}$$

                    sec(4*x)                   
-----------------------------------------------
/         sec(3*x)*sec(4*x)     \    /      pi\
|1 + ---------------------------|*sec|4*x - --|
|       /      pi\    /      pi\|    \      2 /
|    sec|3*x - --|*sec|4*x - --||              
\       \      2 /    \      2 //

$$\frac{\sec{\left(4 x \right)}}{\left(\frac{\sec{\left(3 x \right)} \sec{\left(4 x \right)}}{\sec{\left(3 x - \frac{\pi}{2} \right)} \sec{\left(4 x - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(4 x - \frac{\pi}{2} \right)}}$$

               1                
--------------------------------
/            1        \         
|1 + -----------------|*cot(4*x)
\    cot(3*x)*cot(4*x)/

$$\frac{1}{\left(1 + \frac{1}{\cot{\left(3 x \right)} \cot{\left(4 x \right)}}\right) \cot{\left(4 x \right)}}$$

            sin(4*x)            
--------------------------------
(1 + tan(3*x)*tan(4*x))*cos(4*x)

$$\frac{\sin{\left(4 x \right)}}{\left(\tan{\left(3 x \right)} \tan{\left(4 x \right)} + 1\right) \cos{\left(4 x \right)}}$$

   2      /       2/      pi\\         
sin (2*x)*|1 + tan |2*x + --||*cot(2*x)
          \        \      4 //         
---------------------------------------
                            /      pi\ 
 (1 + tan(3*x)*tan(4*x))*tan|2*x + --| 
                            \      4 /

$$\frac{\left(\tan^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right) \sin^{2}{\left(2 x \right)} \cot{\left(2 x \right)}}{\left(\tan{\left(3 x \right)} \tan{\left(4 x \right)} + 1\right) \tan{\left(2 x + \frac{\pi}{4} \right)}}$$

            sin(4*x)            
--------------------------------
/    sin(3*x)*sin(4*x)\         
|1 + -----------------|*cos(4*x)
\    cos(3*x)*cos(4*x)/

$$\frac{\sin{\left(4 x \right)}}{\left(\frac{\sin{\left(3 x \right)} \sin{\left(4 x \right)}}{\cos{\left(3 x \right)} \cos{\left(4 x \right)}} + 1\right) \cos{\left(4 x \right)}}$$

                                2         4                                         
                           4*cot (2*x)*sin (2*x)*tan(4*x)                           
------------------------------------------------------------------------------------
/                             -cos(7*x) + cos(x)                         \    2     
|1 + --------------------------------------------------------------------|*sin (4*x)
|      /                                                      2         \|          
\    2*\-3*cos(3*x) + 2*cos(x) + 2*cos(5*x) + 2*(1 - cos(2*x)) *cos(3*x)//

$$\frac{4 \sin^{4}{\left(2 x \right)} \tan{\left(4 x \right)} \cot^{2}{\left(2 x \right)}}{\left(\frac{\cos{\left(x \right)} - \cos{\left(7 x \right)}}{2 \left(2 \left(1 - \cos{\left(2 x \right)}\right)^{2} \cos{\left(3 x \right)} + 2 \cos{\left(x \right)} - 3 \cos{\left(3 x \right)} + 2 \cos{\left(5 x \right)}\right)} + 1\right) \sin^{2}{\left(4 x \right)}}$$

            2         /      pi\       
       2*sin (4*x)*sec|8*x - --|       
                      \      2 /       
---------------------------------------
         2         2         /      pi\
    4*sin (3*x)*sin (4*x)*sec|8*x - --|
                             \      2 /
1 + -----------------------------------
                  sin(6*x)

$$\frac{2 \sin^{2}{\left(4 x \right)} \sec{\left(8 x - \frac{\pi}{2} \right)}}{\frac{4 \sin^{2}{\left(3 x \right)} \sin^{2}{\left(4 x \right)} \sec{\left(8 x - \frac{\pi}{2} \right)}}{\sin{\left(6 x \right)}} + 1}$$

                                  2      /       2     \                              
                             4*cot (2*x)*\1 + cot (4*x)/                              
--------------------------------------------------------------------------------------
                 /          2         2/3*x\ /       2     \ /       2     \\         
               2 |    16*cot (2*x)*cot |---|*\1 + cot (3*x)/*\1 + cot (4*x)/|         
/       2     \  |                     \ 2 /                                |         
\1 + cot (2*x)/ *|1 + ------------------------------------------------------|*cot(4*x)
                 |                    2                2                    |         
                 |     /       2     \  /       2/3*x\\                     |         
                 |     \1 + cot (2*x)/ *|1 + cot |---|| *cot(3*x)*cot(4*x)  |         
                 \                      \        \ 2 //                     /

$$\frac{4 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(2 x \right)}}{\left(1 + \frac{16 \left(\cot^{2}{\left(3 x \right)} + 1\right) \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(\frac{3 x}{2} \right)} \cot^{2}{\left(2 x \right)}}{\left(\cot^{2}{\left(\frac{3 x}{2} \right)} + 1\right)^{2} \left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(3 x \right)} \cot{\left(4 x \right)}}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(4 x \right)}}$$

                 /      pi\               
              cos|4*x - --|               
                 \      2 /               
------------------------------------------
/       /      pi\    /      pi\\         
|    cos|3*x - --|*cos|4*x - --||         
|       \      2 /    \      2 /|         
|1 + ---------------------------|*cos(4*x)
\         cos(3*x)*cos(4*x)     /

$$\frac{\cos{\left(4 x - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos{\left(3 x - \frac{\pi}{2} \right)} \cos{\left(4 x - \frac{\pi}{2} \right)}}{\cos{\left(3 x \right)} \cos{\left(4 x \right)}}\right) \cos{\left(4 x \right)}}$$

                 sec(4*x)                 
------------------------------------------
/       /pi      \    /pi      \\         
|    csc|-- - 4*x|*csc|-- - 3*x||         
|       \2       /    \2       /|         
|1 + ---------------------------|*csc(4*x)
\         csc(3*x)*csc(4*x)     /

$$\frac{\sec{\left(4 x \right)}}{\left(1 + \frac{\csc{\left(- 4 x + \frac{\pi}{2} \right)} \csc{\left(- 3 x + \frac{\pi}{2} \right)}}{\csc{\left(3 x \right)} \csc{\left(4 x \right)}}\right) \csc{\left(4 x \right)}}$$

                                  2      /       2     \                              
                             4*tan (2*x)*\1 + tan (4*x)/                              
--------------------------------------------------------------------------------------
                 /          2         2/3*x\ /       2     \ /       2     \\         
               2 |    16*tan (2*x)*tan |---|*\1 + tan (3*x)/*\1 + tan (4*x)/|         
/       2     \  |                     \ 2 /                                |         
\1 + tan (2*x)/ *|1 + ------------------------------------------------------|*tan(4*x)
                 |                    2                2                    |         
                 |     /       2     \  /       2/3*x\\                     |         
                 |     \1 + tan (2*x)/ *|1 + tan |---|| *tan(3*x)*tan(4*x)  |         
                 \                      \        \ 2 //                     /

$$\frac{4 \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan^{2}{\left(2 x \right)}}{\left(1 + \frac{16 \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan^{2}{\left(\frac{3 x}{2} \right)} \tan^{2}{\left(2 x \right)}}{\left(\tan^{2}{\left(\frac{3 x}{2} \right)} + 1\right)^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \tan{\left(3 x \right)} \tan{\left(4 x \right)}}\right) \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \tan{\left(4 x \right)}}$$

                 2                         
            2*sin (4*x)*csc(8*x)           
-------------------------------------------
         2         2                       
1 + 4*sin (3*x)*sin (4*x)*csc(6*x)*csc(8*x)

$$\frac{2 \sin^{2}{\left(4 x \right)} \csc{\left(8 x \right)}}{4 \sin^{2}{\left(3 x \right)} \sin^{2}{\left(4 x \right)} \csc{\left(6 x \right)} \csc{\left(8 x \right)} + 1}$$

  sec(4*x)*sin(4*x)  
---------------------
1 + tan(3*x)*tan(4*x)

$$\frac{\sin{\left(4 x \right)} \sec{\left(4 x \right)}}{\tan{\left(3 x \right)} \tan{\left(4 x \right)} + 1}$$

              sin(4*x)              
------------------------------------
/         2         2     \         
|    4*sin (3*x)*sin (4*x)|         
|1 + ---------------------|*cos(4*x)
\      sin(6*x)*sin(8*x)  /

$$\frac{\sin{\left(4 x \right)}}{\left(\frac{4 \sin^{2}{\left(3 x \right)} \sin^{2}{\left(4 x \right)}}{\sin{\left(6 x \right)} \sin{\left(8 x \right)}} + 1\right) \cos{\left(4 x \right)}}$$

                      /      pi\                  
                 2*sec|8*x - --|                  
                      \      2 /                  
--------------------------------------------------
/         /      pi\    /      pi\\               
|    4*sec|6*x - --|*sec|8*x - --||               
|         \      2 /    \      2 /|    2/      pi\
|1 + -----------------------------|*sec |4*x - --|
|       2/      pi\    2/      pi\|     \      2 /
|    sec |3*x - --|*sec |4*x - --||               
\        \      2 /     \      2 //

$$\frac{2 \sec{\left(8 x - \frac{\pi}{2} \right)}}{\left(1 + \frac{4 \sec{\left(6 x - \frac{\pi}{2} \right)} \sec{\left(8 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(3 x - \frac{\pi}{2} \right)} \sec^{2}{\left(4 x - \frac{\pi}{2} \right)}}\right) \sec^{2}{\left(4 x - \frac{\pi}{2} \right)}}$$

                                         4         2                                         
                                    4*cos (2*x)*tan (2*x)                                    
---------------------------------------------------------------------------------------------
/                             -cos(7*x) + cos(x)                         \    2              
|1 + --------------------------------------------------------------------|*cos (4*x)*tan(4*x)
|      /                                                      2         \|                   
\    2*\-3*cos(3*x) + 2*cos(x) + 2*cos(5*x) + 2*(1 - cos(2*x)) *cos(3*x)//

$$\frac{4 \cos^{4}{\left(2 x \right)} \tan^{2}{\left(2 x \right)}}{\left(\frac{\cos{\left(x \right)} - \cos{\left(7 x \right)}}{2 \left(2 \left(1 - \cos{\left(2 x \right)}\right)^{2} \cos{\left(3 x \right)} + 2 \cos{\left(x \right)} - 3 \cos{\left(3 x \right)} + 2 \cos{\left(5 x \right)}\right)} + 1\right) \cos^{2}{\left(4 x \right)} \tan{\left(4 x \right)}}$$

                       2/      pi\                 
                  2*cos |4*x - --|                 
                        \      2 /                 
---------------------------------------------------
/         2/      pi\    2/      pi\\              
|    4*cos |3*x - --|*cos |4*x - --||              
|          \      2 /     \      2 /|    /      pi\
|1 + -------------------------------|*cos|8*x - --|
|         /      pi\    /      pi\  |    \      2 /
|      cos|6*x - --|*cos|8*x - --|  |              
\         \      2 /    \      2 /  /

$$\frac{2 \cos^{2}{\left(4 x - \frac{\pi}{2} \right)}}{\left(\frac{4 \cos^{2}{\left(3 x - \frac{\pi}{2} \right)} \cos^{2}{\left(4 x - \frac{\pi}{2} \right)}}{\cos{\left(6 x - \frac{\pi}{2} \right)} \cos{\left(8 x - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(8 x - \frac{\pi}{2} \right)}}$$

               2*cot(2*x)               
----------------------------------------
                        /        2     \
(1 + tan(3*x)*tan(4*x))*\-1 + cot (2*x)/

$$\frac{2 \cot{\left(2 x \right)}}{\left(\tan{\left(3 x \right)} \tan{\left(4 x \right)} + 1\right) \left(\cot^{2}{\left(2 x \right)} - 1\right)}$$

2*cot(2*x)/((1 + tan(3*x)*tan(4*x))*(-1 + cot(2*x)^2))

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¿Cómo vas a descomponer esta tg4x/(1+tg4x*tg3x) expresión en fracciones?

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