Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(12/x^7)/(7*(3-6*cos(12/x^7)+3*cos(12/x^7)^2+3*sin(12/x^7)^2))
¿Cómo vas a descomponer esta sin(12/x^7)/(7*(3-6*cos(12/x^7)+3*cos(12/x^7)^2+3*sin(12/x^7)^2)) expresión en fracciones?
Solución
Ha introducido
[src]
/12\
sin|--|
| 7|
\x /
-------------------------------------------
/ /12\ 2/12\ 2/12\\
7*|3 - 6*cos|--| + 3*cos |--| + 3*sin |--||
| | 7| | 7| | 7||
\ \x / \x / \x //
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{7 \left(\left(\left(3 - 6 \cos{\left(\frac{12}{x^{7}} \right)}\right) + 3 \cos^{2}{\left(\frac{12}{x^{7}} \right)}\right) + 3 \sin^{2}{\left(\frac{12}{x^{7}} \right)}\right)}$$
sin(12/x^7)/((7*(3 - 6*cos(12/x^7) + 3*cos(12/x^7)^2 + 3*sin(12/x^7)^2)))
Simplificación general
[src]
1
----------
/6 \
42*tan|--|
| 7|
\x /
$$\frac{1}{42 \tan{\left(\frac{6}{x^{7}} \right)}}$$
1/(42*tan(6/x^7))
Respuesta numérica
[src]
sin(12/x^7)/(21.0 + 21.0*cos(12/x^7)^2 + 21.0*sin(12/x^7)^2 - 42.0*cos(12/x^7))
sin(12/x^7)/(21.0 + 21.0*cos(12/x^7)^2 + 21.0*sin(12/x^7)^2 - 42.0*cos(12/x^7))
Unión de expresiones racionales
[src]
/12\
sin|--|
| 7|
\x /
----------------------------------------
/ 2/12\ 2/12\ /12\\
21*|1 + cos |--| + sin |--| - 2*cos|--||
| | 7| | 7| | 7||
\ \x / \x / \x //
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{21 \left(\sin^{2}{\left(\frac{12}{x^{7}} \right)} + \cos^{2}{\left(\frac{12}{x^{7}} \right)} - 2 \cos{\left(\frac{12}{x^{7}} \right)} + 1\right)}$$
sin(12/x^7)/(21*(1 + cos(12/x^7)^2 + sin(12/x^7)^2 - 2*cos(12/x^7)))
Combinatoria
[src]
/12\
sin|--|
| 7|
\x /
----------------------------------------
/ 2/12\ 2/12\ /12\\
21*|1 + cos |--| + sin |--| - 2*cos|--||
| | 7| | 7| | 7||
\ \x / \x / \x //
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{21 \left(\sin^{2}{\left(\frac{12}{x^{7}} \right)} + \cos^{2}{\left(\frac{12}{x^{7}} \right)} - 2 \cos{\left(\frac{12}{x^{7}} \right)} + 1\right)}$$
sin(12/x^7)/(21*(1 + cos(12/x^7)^2 + sin(12/x^7)^2 - 2*cos(12/x^7)))
Potencias
[src]
/ -12*I 12*I\
| ----- ----|
| 7 7 |
| x x |
-I*\- e + e /
-----------------------------------------------------------------------------
/ 2 2\
| / -12*I 12*I\ / -12*I 12*I\ |
| -12*I 12*I | ----- ----| | ----- ----| |
| ----- ---- | 7 7 | | 7 7 | |
| 7 7 | x x | | x x | |
| x x |e e | 21*\- e + e / |
2*|21 - 21*e - 21*e + 21*|------ + -----| - ----------------------|
\ \ 2 2 / 4 /
$$- \frac{i \left(e^{\frac{12 i}{x^{7}}} - e^{- \frac{12 i}{x^{7}}}\right)}{2 \left(21 \left(\frac{e^{\frac{12 i}{x^{7}}}}{2} + \frac{e^{- \frac{12 i}{x^{7}}}}{2}\right)^{2} - \frac{21 \left(e^{\frac{12 i}{x^{7}}} - e^{- \frac{12 i}{x^{7}}}\right)^{2}}{4} - 21 e^{\frac{12 i}{x^{7}}} + 21 - 21 e^{- \frac{12 i}{x^{7}}}\right)}$$
/12\
sin|--|
| 7|
\x /
-------------------------------------------
/12\ 2/12\ 2/12\
21 - 42*cos|--| + 21*cos |--| + 21*sin |--|
| 7| | 7| | 7|
\x / \x / \x /
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{21 \sin^{2}{\left(\frac{12}{x^{7}} \right)} + 21 \cos^{2}{\left(\frac{12}{x^{7}} \right)} - 42 \cos{\left(\frac{12}{x^{7}} \right)} + 21}$$
sin(12/x^7)/(21 - 42*cos(12/x^7) + 21*cos(12/x^7)^2 + 21*sin(12/x^7)^2)
Denominador común
[src]
/12\
sin|--|
| 7|
\x /
-------------------------------------------
/12\ 2/12\ 2/12\
21 - 42*cos|--| + 21*cos |--| + 21*sin |--|
| 7| | 7| | 7|
\x / \x / \x /
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{21 \sin^{2}{\left(\frac{12}{x^{7}} \right)} + 21 \cos^{2}{\left(\frac{12}{x^{7}} \right)} - 42 \cos{\left(\frac{12}{x^{7}} \right)} + 21}$$
sin(12/x^7)/(21 - 42*cos(12/x^7) + 21*cos(12/x^7)^2 + 21*sin(12/x^7)^2)
Denominador racional
[src]
/12\
sin|--|
| 7|
\x /
-------------------------------------------
/12\ 2/12\ 2/12\
21 - 42*cos|--| + 21*cos |--| + 21*sin |--|
| 7| | 7| | 7|
\x / \x / \x /
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{21 \sin^{2}{\left(\frac{12}{x^{7}} \right)} + 21 \cos^{2}{\left(\frac{12}{x^{7}} \right)} - 42 \cos{\left(\frac{12}{x^{7}} \right)} + 21}$$
sin(12/x^7)/(21 - 42*cos(12/x^7) + 21*cos(12/x^7)^2 + 21*sin(12/x^7)^2)
Parte trigonométrica
[src]
/6 \
2*tan|--|
| 7|
\x /
------------------------------------------------------------------------------
/ 2 \
| / 2/6 \\ / 2/6 \\ 2/6 \ |
| 42*|1 - tan |--|| 21*|1 - tan |--|| 84*tan |--| |
| | | 7|| | | 7|| | 7| |
/ 2/6 \\ | \ \x // \ \x // \x / |
|1 + tan |--||*|21 - ----------------- + ------------------ + ---------------|
| | 7|| | 2/6 \ 2 2|
\ \x // | 1 + tan |--| / 2/6 \\ / 2/6 \\ |
| | 7| |1 + tan |--|| |1 + tan |--|| |
| \x / | | 7|| | | 7|| |
\ \ \x // \ \x // /
$$\frac{2 \tan{\left(\frac{6}{x^{7}} \right)}}{\left(\tan^{2}{\left(\frac{6}{x^{7}} \right)} + 1\right) \left(\frac{21 \left(1 - \tan^{2}{\left(\frac{6}{x^{7}} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{6}{x^{7}} \right)} + 1\right)^{2}} - \frac{42 \left(1 - \tan^{2}{\left(\frac{6}{x^{7}} \right)}\right)}{\tan^{2}{\left(\frac{6}{x^{7}} \right)} + 1} + 21 + \frac{84 \tan^{2}{\left(\frac{6}{x^{7}} \right)}}{\left(\tan^{2}{\left(\frac{6}{x^{7}} \right)} + 1\right)^{2}}\right)}$$
/6 \ cot|--| | 7| \x / ------- 42
$$\frac{\cot{\left(\frac{6}{x^{7}} \right)}}{42}$$
/12\
sin|--|
| 7|
\x /
-------------------------------------------
/12\ 2/12\ 2/12\
21 - 42*cos|--| + 21*cos |--| + 21*sin |--|
| 7| | 7| | 7|
\x / \x / \x /
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{21 \sin^{2}{\left(\frac{12}{x^{7}} \right)} + 21 \cos^{2}{\left(\frac{12}{x^{7}} \right)} - 42 \cos{\left(\frac{12}{x^{7}} \right)} + 21}$$
1 ------------------------------------------------------ / 42 21 21 \ /12\ |21 - ------------ + -------- + -------------|*csc|--| | /pi 12\ 2/12\ 2/pi 12\| | 7| | csc|-- - --| csc |--| csc |-- - --|| \x / | |2 7| | 7| |2 7|| \ \ x / \x / \ x //
$$\frac{1}{\left(21 - \frac{42}{\csc{\left(\frac{\pi}{2} - \frac{12}{x^{7}} \right)}} + \frac{21}{\csc^{2}{\left(\frac{\pi}{2} - \frac{12}{x^{7}} \right)}} + \frac{21}{\csc^{2}{\left(\frac{12}{x^{7}} \right)}}\right) \csc{\left(\frac{12}{x^{7}} \right)}}$$
/12\
sin|--|
| 7|
\x /
-----------
2/6 \
84*sin |--|
| 7|
\x /
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{84 \sin^{2}{\left(\frac{6}{x^{7}} \right)}}$$
1 ------------------------------------------------------ / 42 21 21 \ /12 pi\ |21 - ------- + -------- + -------------|*sec|-- - --| | /12\ 2/12\ 2/12 pi\| | 7 2 | | sec|--| sec |--| sec |-- - --|| \x / | | 7| | 7| | 7 2 || \ \x / \x / \x //
$$\frac{1}{\left(21 + \frac{21}{\sec^{2}{\left(- \frac{\pi}{2} + \frac{12}{x^{7}} \right)}} - \frac{42}{\sec{\left(\frac{12}{x^{7}} \right)}} + \frac{21}{\sec^{2}{\left(\frac{12}{x^{7}} \right)}}\right) \sec{\left(- \frac{\pi}{2} + \frac{12}{x^{7}} \right)}}$$
/6 pi\
sec|-- - --|
| 7 2 |
\x /
------------
/6 \
42*sec|--|
| 7|
\x /
$$\frac{\sec{\left(- \frac{\pi}{2} + \frac{6}{x^{7}} \right)}}{42 \sec{\left(\frac{6}{x^{7}} \right)}}$$
/12 pi\
cos|-- - --|
| 7 2 |
\x /
------------------------------------------------
/12\ 2/12\ 2/12 pi\
21 - 42*cos|--| + 21*cos |--| + 21*cos |-- - --|
| 7| | 7| | 7 2 |
\x / \x / \x /
$$\frac{\cos{\left(- \frac{\pi}{2} + \frac{12}{x^{7}} \right)}}{21 \cos^{2}{\left(\frac{12}{x^{7}} \right)} - 42 \cos{\left(\frac{12}{x^{7}} \right)} + 21 \cos^{2}{\left(- \frac{\pi}{2} + \frac{12}{x^{7}} \right)} + 21}$$
/12\
sin|--|
| 7|
\x /
-----------------------------------------------------
/pi 12\ 2/12\ 2/pi 12\
21 - 42*sin|-- + --| + 21*sin |--| + 21*sin |-- + --|
|2 7| | 7| |2 7|
\ x / \x / \ x /
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{21 \sin^{2}{\left(\frac{12}{x^{7}} \right)} + 21 \sin^{2}{\left(\frac{\pi}{2} + \frac{12}{x^{7}} \right)} - 42 \sin{\left(\frac{\pi}{2} + \frac{12}{x^{7}} \right)} + 21}$$
/6 \
cos|--|
| 7|
\x /
---------------
/6 pi\
42*cos|-- - --|
| 7 2 |
\x /
$$\frac{\cos{\left(\frac{6}{x^{7}} \right)}}{42 \cos{\left(- \frac{\pi}{2} + \frac{6}{x^{7}} \right)}}$$
/6 \
2*cot|--|
| 7|
\x /
--------------------------------------------------------------------------------
/ 2 \
| / 2/6 \\ / 2/6 \\ 2/6 \ |
| 42*|-1 + cot |--|| 21*|-1 + cot |--|| 84*cot |--| |
| | | 7|| | | 7|| | 7| |
/ 2/6 \\ | \ \x // \ \x // \x / |
|1 + cot |--||*|21 - ------------------ + ------------------- + ---------------|
| | 7|| | 2/6 \ 2 2|
\ \x // | 1 + cot |--| / 2/6 \\ / 2/6 \\ |
| | 7| |1 + cot |--|| |1 + cot |--|| |
| \x / | | 7|| | | 7|| |
\ \ \x // \ \x // /
$$\frac{2 \cot{\left(\frac{6}{x^{7}} \right)}}{\left(\cot^{2}{\left(\frac{6}{x^{7}} \right)} + 1\right) \left(\frac{21 \left(\cot^{2}{\left(\frac{6}{x^{7}} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{6}{x^{7}} \right)} + 1\right)^{2}} - \frac{42 \left(\cot^{2}{\left(\frac{6}{x^{7}} \right)} - 1\right)}{\cot^{2}{\left(\frac{6}{x^{7}} \right)} + 1} + 21 + \frac{84 \cot^{2}{\left(\frac{6}{x^{7}} \right)}}{\left(\cot^{2}{\left(\frac{6}{x^{7}} \right)} + 1\right)^{2}}\right)}$$
/6 \
csc|--|
| 7|
\x /
---------------
/pi 6 \
42*csc|-- - --|
|2 7|
\ x /
$$\frac{\csc{\left(\frac{6}{x^{7}} \right)}}{42 \csc{\left(\frac{\pi}{2} - \frac{6}{x^{7}} \right)}}$$
1
----------
/6 \
42*tan|--|
| 7|
\x /
$$\frac{1}{42 \tan{\left(\frac{6}{x^{7}} \right)}}$$
1 -------------------------------------------- / 42 21 21 \ /12\ |21 - ------- + -------- + --------|*csc|--| | /12\ 2/12\ 2/12\| | 7| | sec|--| csc |--| sec |--|| \x / | | 7| | 7| | 7|| \ \x / \x / \x //
$$\frac{1}{\left(21 - \frac{42}{\sec{\left(\frac{12}{x^{7}} \right)}} + \frac{21}{\sec^{2}{\left(\frac{12}{x^{7}} \right)}} + \frac{21}{\csc^{2}{\left(\frac{12}{x^{7}} \right)}}\right) \csc{\left(\frac{12}{x^{7}} \right)}}$$
1/((21 - 42/sec(12/x^7) + 21/csc(12/x^7)^2 + 21/sec(12/x^7)^2)*csc(12/x^7))
Compilar la expresión
[src]
/12\
sin|--|
| 7|
\x /
-------------------------------------------
/12\ 2/12\ 2/12\
21 - 42*cos|--| + 21*cos |--| + 21*sin |--|
| 7| | 7| | 7|
\x / \x / \x /
$$\frac{\sin{\left(\frac{12}{x^{7}} \right)}}{21 \sin^{2}{\left(\frac{12}{x^{7}} \right)} + 21 \cos^{2}{\left(\frac{12}{x^{7}} \right)} - 42 \cos{\left(\frac{12}{x^{7}} \right)} + 21}$$
sin(12/x^7)/(21 - 42*cos(12/x^7) + 21*cos(12/x^7)^2 + 21*sin(12/x^7)^2)