Sr Examen
¿Cómo vas a descomponer esta sin(2*x)/(2*sin(x)-cos(x)) expresión en fracciones?
Solución
Ha introducido
[src]
sin(2*x) ----------------- 2*sin(x) - cos(x)
$$\frac{\sin{\left(2 x \right)}}{2 \sin{\left(x \right)} - \cos{\left(x \right)}}$$
sin(2*x)/(2*sin(x) - cos(x))
Combinatoria
[src]
-sin(2*x) ------------------ -2*sin(x) + cos(x)
$$- \frac{\sin{\left(2 x \right)}}{- 2 \sin{\left(x \right)} + \cos{\left(x \right)}}$$
-sin(2*x)/(-2*sin(x) + cos(x))
Denominador común
[src]
-sin(2*x) ------------------ -2*sin(x) + cos(x)
$$- \frac{\sin{\left(2 x \right)}}{- 2 \sin{\left(x \right)} + \cos{\left(x \right)}}$$
-sin(2*x)/(-2*sin(x) + cos(x))
Potencias
[src]
/ -2*I*x 2*I*x\
-I*\- e + e /
---------------------------------------
/ I*x -I*x \
| e e / -I*x I*x\|
2*|- ---- - ----- - I*\- e + e /|
\ 2 2 /
$$- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2 \left(- i \left(e^{i x} - e^{- i x}\right) - \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}\right)}$$
-i*(-exp(-2*i*x) + exp(2*i*x))/(2*(-exp(i*x)/2 - exp(-i*x)/2 - i*(-exp(-i*x) + exp(i*x))))
Parte trigonométrica
[src]
-1 ------------------------------------ / 1 2 \ / pi\ |------ - -----------|*sec|2*x - --| |sec(x) / pi\| \ 2 / | sec|x - --|| \ \ 2 //
$$- \frac{1}{\left(- \frac{2}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
2*cot(x)
--------------------------------------------
/ 2/x\ /x\ \
| -1 + cot |-| 4*cot|-| |
/ 2 \ | \2/ \2/ |
\1 + cot (x)/*|- ------------ + -----------|
| 2/x\ 2/x\|
| 1 + cot |-| 1 + cot |-||
\ \2/ \2//
$$\frac{2 \cot{\left(x \right)}}{\left(- \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{4 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}$$
sin(2*x)
------------------------
/ pi\
- sin|x + --| + 2*sin(x)
\ 2 /
$$\frac{\sin{\left(2 x \right)}}{2 \sin{\left(x \right)} - \sin{\left(x + \frac{\pi}{2} \right)}}$$
1 -------------------------------------- / 1 2 \ / pi\ |- ------ + -----------|*sec|2*x - --| | sec(x) / pi\| \ 2 / | sec|x - --|| \ \ 2 //
$$\frac{1}{\left(\frac{2}{\sec{\left(x - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
1 --------------------------------- / 1 2 \ |- ----------- + ------|*csc(2*x) | /pi \ csc(x)| | csc|-- - x| | \ \2 / /
$$\frac{1}{\left(- \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{2}{\csc{\left(x \right)}}\right) \csc{\left(2 x \right)}}$$
/ pi\
cos|2*x - --|
\ 2 /
-----------------------
/ pi\
-cos(x) + 2*cos|x - --|
\ 2 /
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{- \cos{\left(x \right)} + 2 \cos{\left(x - \frac{\pi}{2} \right)}}$$
2*tan(x)
-------------------------------------------
/ 2/x\ /x\ \
| 1 - tan |-| 4*tan|-| |
/ 2 \ | \2/ \2/ |
\1 + tan (x)/*|- ----------- + -----------|
| 2/x\ 2/x\|
| 1 + tan |-| 1 + tan |-||
\ \2/ \2//
$$\frac{2 \tan{\left(x \right)}}{\left(- \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{4 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}$$
-1 ------------------------------- / 1 2 \ |----------- - ------|*csc(2*x) | /pi \ csc(x)| |csc|-- - x| | \ \2 / /
$$- \frac{1}{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{2}{\csc{\left(x \right)}}\right) \csc{\left(2 x \right)}}$$
/ pi\
-cos|2*x - --|
\ 2 /
------------------------
/ pi\
- 2*cos|x - --| + cos(x)
\ 2 /
$$- \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} - 2 \cos{\left(x - \frac{\pi}{2} \right)}}$$
-2*cot(x)
------------------------------------------
/ 2/x\ /x\ \
|-1 + cot |-| 4*cot|-| |
/ 2 \ | \2/ \2/ |
\1 + cot (x)/*|------------ - -----------|
| 2/x\ 2/x\|
|1 + cot |-| 1 + cot |-||
\ \2/ \2//
$$- \frac{2 \cot{\left(x \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{4 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}$$
-2*tan(x)
-----------------------------------------
/ 2/x\ /x\ \
|1 - tan |-| 4*tan|-| |
/ 2 \ | \2/ \2/ |
\1 + tan (x)/*|----------- - -----------|
| 2/x\ 2/x\|
|1 + tan |-| 1 + tan |-||
\ \2/ \2//
$$- \frac{2 \tan{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{4 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}$$
-sin(2*x) ------------------ -2*sin(x) + cos(x)
$$- \frac{\sin{\left(2 x \right)}}{- 2 \sin{\left(x \right)} + \cos{\left(x \right)}}$$
1 ---------------------------- / 1 2 \ |- ------ + ------|*csc(2*x) \ sec(x) csc(x)/
$$\frac{1}{\left(- \frac{1}{\sec{\left(x \right)}} + \frac{2}{\csc{\left(x \right)}}\right) \csc{\left(2 x \right)}}$$
-sin(2*x)
-----------------------
/ pi\
-2*sin(x) + sin|x + --|
\ 2 /
$$- \frac{\sin{\left(2 x \right)}}{- 2 \sin{\left(x \right)} + \sin{\left(x + \frac{\pi}{2} \right)}}$$
-sin(2*x)/(-2*sin(x) + sin(x + pi/2))