Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(x)/((tan(pi/4)-(x/2))*(1+sin(x)))
¿Cómo vas a descomponer esta sin(x)/((tan(pi/4)-(x/2))*(1+sin(x))) expresión en fracciones?
Solución
Ha introducido
[src]
sin(x) -------------------------- / /pi\ x\ |tan|--| - -|*(1 + sin(x)) \ \4 / 2/
$$\frac{\sin{\left(x \right)}}{\left(- \frac{x}{2} + \tan{\left(\frac{\pi}{4} \right)}\right) \left(\sin{\left(x \right)} + 1\right)}$$
sin(x)/(((tan(pi/4) - x/2)*(1 + sin(x))))
Simplificación general
[src]
-2*sin(x) --------------------- (1 + sin(x))*(-2 + x)
$$- \frac{2 \sin{\left(x \right)}}{\left(x - 2\right) \left(\sin{\left(x \right)} + 1\right)}$$
-2*sin(x)/((1 + sin(x))*(-2 + x))
Denominador común
[src]
-2*sin(x) ---------------------------- -2 + x - 2*sin(x) + x*sin(x)
$$- \frac{2 \sin{\left(x \right)}}{x \sin{\left(x \right)} + x - 2 \sin{\left(x \right)} - 2}$$
-2*sin(x)/(-2 + x - 2*sin(x) + x*sin(x))
Denominador racional
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2*sin(x)
-----------------------------
/ /pi\\
(1 + sin(x))*|-x + 2*tan|--||
\ \4 //
$$\frac{2 \sin{\left(x \right)}}{\left(- x + 2 \tan{\left(\frac{\pi}{4} \right)}\right) \left(\sin{\left(x \right)} + 1\right)}$$
2*sin(x)/((1 + sin(x))*(-x + 2*tan(pi/4)))
Combinatoria
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-2*sin(x) --------------------- (1 + sin(x))*(-2 + x)
$$- \frac{2 \sin{\left(x \right)}}{\left(x - 2\right) \left(\sin{\left(x \right)} + 1\right)}$$
-2*sin(x)/((1 + sin(x))*(-2 + x))
Respuesta numérica
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sin(x)/((1.0 - 0.5*x)*(1.0 + sin(x)))
sin(x)/((1.0 - 0.5*x)*(1.0 + sin(x)))
Unión de expresiones racionales
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2*sin(x) -------------------- (1 + sin(x))*(2 - x)
$$\frac{2 \sin{\left(x \right)}}{\left(2 - x\right) \left(\sin{\left(x \right)} + 1\right)}$$
2*sin(x)/((1 + sin(x))*(2 - x))
Potencias
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/ -I*x I*x\
-I*\- e + e /
--------------------------------------------------------
/ / pi*I -pi*I \\
| | ---- ------||
/ / -I*x I*x\\ | | 4 4 ||
| I*\- e + e /| | x I*\- e + e /|
2*|1 - ------------------|*|- - + ---------------------|
\ 2 / | 2 -pi*I pi*I |
| ------ ---- |
| 4 4 |
\ e + e /
$$- \frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(- \frac{x}{2} + \frac{i \left(- e^{\frac{i \pi}{4}} + e^{- \frac{i \pi}{4}}\right)}{e^{- \frac{i \pi}{4}} + e^{\frac{i \pi}{4}}}\right) \left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1\right)}$$
sin(x) -------------------- / x\ |1 - -|*(1 + sin(x)) \ 2/
$$\frac{\sin{\left(x \right)}}{\left(1 - \frac{x}{2}\right) \left(\sin{\left(x \right)} + 1\right)}$$
sin(x)/((1 - x/2)*(1 + sin(x)))
Parte trigonométrica
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1 ------------------------------------- / 1 \ / x\ / pi\ |1 + -----------|*|1 - -|*sec|x - --| | / pi\| \ 2/ \ 2 / | sec|x - --|| \ \ 2 //
$$\frac{1}{\left(1 - \frac{x}{2}\right) \left(1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}$$
sin(x) -------------------- / x\ |1 - -|*(1 + sin(x)) \ 2/
$$\frac{\sin{\left(x \right)}}{\left(- \frac{x}{2} + 1\right) \left(\sin{\left(x \right)} + 1\right)}$$
/ pi\
cos|x - --|
\ 2 /
-------------------------
/ x\ / / pi\\
|1 - -|*|1 + cos|x - --||
\ 2/ \ \ 2 //
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\left(1 - \frac{x}{2}\right) \left(\cos{\left(x - \frac{\pi}{2} \right)} + 1\right)}$$
sin(x) -------------------- / x\ |1 - -|*(1 + sin(x)) \ 2/
$$\frac{\sin{\left(x \right)}}{\left(1 - \frac{x}{2}\right) \left(\sin{\left(x \right)} + 1\right)}$$
/x\
2*tan|-|
\2/
---------------------------------------
/ /x\ \
| 2*tan|-| |
/ 2/x\\ / x\ | \2/ |
|1 + tan |-||*|1 - -|*|1 + -----------|
\ \2// \ 2/ | 2/x\|
| 1 + tan |-||
\ \2//
$$\frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(1 - \frac{x}{2}\right) \left(1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/x\
2*cot|-|
\2/
---------------------------------------
/ /x\ \
| 2*cot|-| |
/ 2/x\\ / x\ | \2/ |
|1 + cot |-||*|1 - -|*|1 + -----------|
\ \2// \ 2/ | 2/x\|
| 1 + cot |-||
\ \2//
$$\frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(1 - \frac{x}{2}\right) \left(1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/ pi\
cos|x - --|
\ 2 /
-----------------------------------------
/ / pi\\ / x ___ /-pi \\
|1 + cos|x - --||*|- - + \/ 2 *cos|----||
\ \ 2 // \ 2 \ 4 //
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\left(- \frac{x}{2} + \sqrt{2} \cos{\left(- \frac{\pi}{4} \right)}\right) \left(\cos{\left(x - \frac{\pi}{2} \right)} + 1\right)}$$
1 --------------------------- / 1 \ / x\ |1 + ------|*|1 - -|*csc(x) \ csc(x)/ \ 2/
$$\frac{1}{\left(1 - \frac{x}{2}\right) \left(1 + \frac{1}{\csc{\left(x \right)}}\right) \csc{\left(x \right)}}$$
1/((1 + 1/csc(x))*(1 - x/2)*csc(x))