Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(-2+x/2)/2-1/(2*tan(-2+x/2))
¿Cómo vas a descomponer esta tan(-2+x/2)/2-1/(2*tan(-2+x/2)) expresión en fracciones?
Solución
Ha introducido
[src]
/ x\
tan|-2 + -|
\ 2/ 1
----------- - -------------
2 / x\
2*tan|-2 + -|
\ 2/
$$\frac{\tan{\left(\frac{x}{2} - 2 \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} - 2 \right)}}$$
tan(-2 + x/2)/2 - 1/(2*tan(-2 + x/2))
Descomposición de una fracción
[src]
tan(-2 + x/2)/2 - 1/(2*tan(-2 + x/2))
$$\frac{\tan{\left(\frac{x}{2} - 2 \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} - 2 \right)}}$$
/ x\
tan|-2 + -|
\ 2/ 1
----------- - -------------
2 / x\
2*tan|-2 + -|
\ 2/
Simplificación general
[src]
2/ x\
-1 + tan |-2 + -|
\ 2/
-----------------
/ x\
2*tan|-2 + -|
\ 2/
$$\frac{\tan^{2}{\left(\frac{x}{2} - 2 \right)} - 1}{2 \tan{\left(\frac{x}{2} - 2 \right)}}$$
(-1 + tan(-2 + x/2)^2)/(2*tan(-2 + x/2))
Respuesta numérica
[src]
0.5*tan(-2 + x/2) - 0.5/tan(-2 + x/2)
0.5*tan(-2 + x/2) - 0.5/tan(-2 + x/2)
Combinatoria
[src]
/ / x\\ / / x\\
|1 + tan|-2 + -||*|-1 + tan|-2 + -||
\ \ 2// \ \ 2//
------------------------------------
/ x\
2*tan|-2 + -|
\ 2/
$$\frac{\left(\tan{\left(\frac{x}{2} - 2 \right)} - 1\right) \left(\tan{\left(\frac{x}{2} - 2 \right)} + 1\right)}{2 \tan{\left(\frac{x}{2} - 2 \right)}}$$
(1 + tan(-2 + x/2))*(-1 + tan(-2 + x/2))/(2*tan(-2 + x/2))
Denominador racional
[src]
2/ x\
-2 + 2*tan |-2 + -|
\ 2/
-------------------
/ x\
4*tan|-2 + -|
\ 2/
$$\frac{2 \tan^{2}{\left(\frac{x}{2} - 2 \right)} - 2}{4 \tan{\left(\frac{x}{2} - 2 \right)}}$$
(-2 + 2*tan(-2 + x/2)^2)/(4*tan(-2 + x/2))
Unión de expresiones racionales
[src]
2/-4 + x\
-1 + tan |------|
\ 2 /
-----------------
/-4 + x\
2*tan|------|
\ 2 /
$$\frac{\tan^{2}{\left(\frac{x - 4}{2} \right)} - 1}{2 \tan{\left(\frac{x - 4}{2} \right)}}$$
(-1 + tan((-4 + x)/2)^2)/(2*tan((-4 + x)/2))
Potencias
[src]
/ / x\ / x\\ / / x\ / x\\ | I*|-2 + -| I*|2 - -|| | I*|-2 + -| I*|2 - -|| | \ 2/ \ 2/| | \ 2/ \ 2/| I*\e + e / I*\- e + e / ------------------------------ + ------------------------------ / / x\ / x\\ / / x\ / x\\ | I*|-2 + -| I*|2 - -|| | I*|-2 + -| I*|2 - -|| | \ 2/ \ 2/| | \ 2/ \ 2/| 2*\- e + e / 2*\e + e /
$$\frac{i \left(e^{i \left(2 - \frac{x}{2}\right)} - e^{i \left(\frac{x}{2} - 2\right)}\right)}{2 \left(e^{i \left(2 - \frac{x}{2}\right)} + e^{i \left(\frac{x}{2} - 2\right)}\right)} + \frac{i \left(e^{i \left(2 - \frac{x}{2}\right)} + e^{i \left(\frac{x}{2} - 2\right)}\right)}{2 \left(e^{i \left(2 - \frac{x}{2}\right)} - e^{i \left(\frac{x}{2} - 2\right)}\right)}$$
i*(exp(i*(-2 + x/2)) + exp(i*(2 - x/2)))/(2*(-exp(i*(-2 + x/2)) + exp(i*(2 - x/2)))) + i*(-exp(i*(-2 + x/2)) + exp(i*(2 - x/2)))/(2*(exp(i*(-2 + x/2)) + exp(i*(2 - x/2))))
Parte trigonométrica
[src]
/ x\ / x\
sec|-2 + -| csc|-2 + -|
\ 2/ \ 2/
------------- - -------------
/ x\ / x\
2*csc|-2 + -| 2*sec|-2 + -|
\ 2/ \ 2/
$$- \frac{\csc{\left(\frac{x}{2} - 2 \right)}}{2 \sec{\left(\frac{x}{2} - 2 \right)}} + \frac{\sec{\left(\frac{x}{2} - 2 \right)}}{2 \csc{\left(\frac{x}{2} - 2 \right)}}$$
/ pi\
-sec|-4 + x - --|
\ 2 /
------------------
sec(-4 + x)
$$- \frac{\sec{\left(x - 4 - \frac{\pi}{2} \right)}}{\sec{\left(x - 4 \right)}}$$
-1 ----------- tan(-4 + x)
$$- \frac{1}{\tan{\left(x - 4 \right)}}$$
-cot(-4 + x)
$$- \cot{\left(x - 4 \right)}$$
2/ x\
sin |-2 + -|
\ 2/ sin(-4 + x)
------------ - --------------
sin(-4 + x) 2/ x\
4*sin |-2 + -|
\ 2/
$$\frac{\sin^{2}{\left(\frac{x}{2} - 2 \right)}}{\sin{\left(x - 4 \right)}} - \frac{\sin{\left(x - 4 \right)}}{4 \sin^{2}{\left(\frac{x}{2} - 2 \right)}}$$
/ pi x\ / x\
csc|2 + -- - -| csc|-2 + -|
\ 2 2/ \ 2/
--------------- - -----------------
/ x\ / pi x\
2*csc|-2 + -| 2*csc|2 + -- - -|
\ 2/ \ 2 2/
$$- \frac{\csc{\left(\frac{x}{2} - 2 \right)}}{2 \csc{\left(- \frac{x}{2} + \frac{\pi}{2} + 2 \right)}} + \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} + 2 \right)}}{2 \csc{\left(\frac{x}{2} - 2 \right)}}$$
/ x pi\ / x\
cos|-2 + - - --| cos|-2 + -|
\ 2 2 / \ 2/
---------------- - ------------------
/ x\ / x pi\
2*cos|-2 + -| 2*cos|-2 + - - --|
\ 2/ \ 2 2 /
$$- \frac{\cos{\left(\frac{x}{2} - 2 \right)}}{2 \cos{\left(\frac{x}{2} - 2 - \frac{\pi}{2} \right)}} + \frac{\cos{\left(\frac{x}{2} - 2 - \frac{\pi}{2} \right)}}{2 \cos{\left(\frac{x}{2} - 2 \right)}}$$
-csc(-4 + x) --------------- / pi \ csc|4 + -- - x| \ 2 /
$$- \frac{\csc{\left(x - 4 \right)}}{\csc{\left(- x + \frac{\pi}{2} + 4 \right)}}$$
/ x\
cot|-2 + -|
1 \ 2/
------------- - -----------
/ x\ 2
2*cot|-2 + -|
\ 2/
$$- \frac{\cot{\left(\frac{x}{2} - 2 \right)}}{2} + \frac{1}{2 \cot{\left(\frac{x}{2} - 2 \right)}}$$
/ x\ / x\
sin|-2 + -| cos|-2 + -|
\ 2/ \ 2/
------------- - -------------
/ x\ / x\
2*cos|-2 + -| 2*sin|-2 + -|
\ 2/ \ 2/
$$\frac{\sin{\left(\frac{x}{2} - 2 \right)}}{2 \cos{\left(\frac{x}{2} - 2 \right)}} - \frac{\cos{\left(\frac{x}{2} - 2 \right)}}{2 \sin{\left(\frac{x}{2} - 2 \right)}}$$
-sin(-8 + 2*x)
---------------
2
2*sin (-4 + x)
$$- \frac{\sin{\left(2 x - 8 \right)}}{2 \sin^{2}{\left(x - 4 \right)}}$$
/ x\ / x\
tan|-2 + -| cot|-2 + -|
\ 2/ \ 2/
----------- - -----------
2 2
$$\frac{\tan{\left(\frac{x}{2} - 2 \right)}}{2} - \frac{\cot{\left(\frac{x}{2} - 2 \right)}}{2}$$
-cos(-4 + x) ---------------- / pi\ cos|-4 + x - --| \ 2 /
$$- \frac{\cos{\left(x - 4 \right)}}{\cos{\left(x - 4 - \frac{\pi}{2} \right)}}$$
/ x\ / x pi\
sec|-2 + -| sec|-2 + - - --|
\ 2/ \ 2 2 /
------------------ - ----------------
/ x pi\ / x\
2*sec|-2 + - - --| 2*sec|-2 + -|
\ 2 2 / \ 2/
$$\frac{\sec{\left(\frac{x}{2} - 2 \right)}}{2 \sec{\left(\frac{x}{2} - 2 - \frac{\pi}{2} \right)}} - \frac{\sec{\left(\frac{x}{2} - 2 - \frac{\pi}{2} \right)}}{2 \sec{\left(\frac{x}{2} - 2 \right)}}$$
sec(-2 + x/2)/(2*sec(-2 + x/2 - pi/2)) - sec(-2 + x/2 - pi/2)/(2*sec(-2 + x/2))