Sr Examen
¿Cómo vas a descomponer esta cos(x)/(1+x)-sin(x)/(1+x)^2 expresión en fracciones?
Solución
Ha introducido
[src]
cos(x) sin(x)
------ - --------
1 + x 2
(1 + x)
$$- \frac{\sin{\left(x \right)}}{\left(x + 1\right)^{2}} + \frac{\cos{\left(x \right)}}{x + 1}$$
cos(x)/(1 + x) - sin(x)/(1 + x)^2
Simplificación general
[src]
-sin(x) + (1 + x)*cos(x)
------------------------
2
(1 + x)
$$\frac{\left(x + 1\right) \cos{\left(x \right)} - \sin{\left(x \right)}}{\left(x + 1\right)^{2}}$$
(-sin(x) + (1 + x)*cos(x))/(1 + x)^2
Denominador racional
[src]
2
(1 + x) *cos(x) - (1 + x)*sin(x)
--------------------------------
3
(1 + x)
$$\frac{\left(x + 1\right)^{2} \cos{\left(x \right)} - \left(x + 1\right) \sin{\left(x \right)}}{\left(x + 1\right)^{3}}$$
((1 + x)^2*cos(x) - (1 + x)*sin(x))/(1 + x)^3
Denominador común
[src]
-sin(x) + x*cos(x) + cos(x)
---------------------------
2
1 + x + 2*x
$$\frac{x \cos{\left(x \right)} - \sin{\left(x \right)} + \cos{\left(x \right)}}{x^{2} + 2 x + 1}$$
(-sin(x) + x*cos(x) + cos(x))/(1 + x^2 + 2*x)
Respuesta numérica
[src]
cos(x)/(1.0 + x) - sin(x)/(1.0 + x)^2
cos(x)/(1.0 + x) - sin(x)/(1.0 + x)^2
Combinatoria
[src]
-sin(x) + x*cos(x) + cos(x)
---------------------------
2
(1 + x)
$$\frac{x \cos{\left(x \right)} - \sin{\left(x \right)} + \cos{\left(x \right)}}{\left(x + 1\right)^{2}}$$
(-sin(x) + x*cos(x) + cos(x))/(1 + x)^2
Potencias
[src]
cos(x) sin(x)
------ - --------
1 + x 2
(1 + x)
$$\frac{\cos{\left(x \right)}}{x + 1} - \frac{\sin{\left(x \right)}}{\left(x + 1\right)^{2}}$$
I*x -I*x
e e
---- + ----- / -I*x I*x\
2 2 I*\- e + e /
------------ + ------------------
1 + x 2
2*(1 + x)
$$\frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{x + 1} + \frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(x + 1\right)^{2}}$$
(exp(i*x)/2 + exp(-i*x)/2)/(1 + x) + i*(-exp(-i*x) + exp(i*x))/(2*(1 + x)^2)
Unión de expresiones racionales
[src]
-sin(x) + (1 + x)*cos(x)
------------------------
2
(1 + x)
$$\frac{\left(x + 1\right) \cos{\left(x \right)} - \sin{\left(x \right)}}{\left(x + 1\right)^{2}}$$
(-sin(x) + (1 + x)*cos(x))/(1 + x)^2
Compilar la expresión
[src]
cos(x) sin(x)
------ - --------
1 + x 2
(1 + x)
$$\frac{\cos{\left(x \right)}}{x + 1} - \frac{\sin{\left(x \right)}}{\left(x + 1\right)^{2}}$$
cos(x)/(1 + x) - sin(x)/(1 + x)^2
Parte trigonométrica
[src]
cos(x) sin(x)
------ - --------
1 + x 2
(1 + x)
$$\frac{\cos{\left(x \right)}}{x + 1} - \frac{\sin{\left(x \right)}}{\left(x + 1\right)^{2}}$$
/ pi\
cos|x - --|
cos(x) \ 2 /
------ - -----------
1 + x 2
(1 + x)
$$\frac{\cos{\left(x \right)}}{x + 1} - \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\left(x + 1\right)^{2}}$$
1 1
-------------- - ---------------
(1 + x)*sec(x) 2
(1 + x) *csc(x)
$$\frac{1}{\left(x + 1\right) \sec{\left(x \right)}} - \frac{1}{\left(x + 1\right)^{2} \csc{\left(x \right)}}$$
2/x\ /x\
1 - tan |-| 2*tan|-|
\2/ \2/
--------------------- - ----------------------
/ 2/x\\ 2 / 2/x\\
(1 + x)*|1 + tan |-|| (1 + x) *|1 + tan |-||
\ \2// \ \2//
$$\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\left(x + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(x + 1\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
2/x\ /x\
-1 + cot |-| 2*cot|-|
\2/ \2/
--------------------- - ----------------------
/ 2/x\\ 2 / 2/x\\
(1 + x)*|1 + cot |-|| (1 + x) *|1 + cot |-||
\ \2// \ \2//
$$\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\left(x + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} - \frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(x + 1\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
1 1
-------------- - --------------------
(1 + x)*sec(x) 2 / pi\
(1 + x) *sec|x - --|
\ 2 /
$$\frac{1}{\left(x + 1\right) \sec{\left(x \right)}} - \frac{1}{\left(x + 1\right)^{2} \sec{\left(x - \frac{\pi}{2} \right)}}$$
/ pi\
sin|x + --|
\ 2 / sin(x)
----------- - --------
1 + x 2
(1 + x)
$$\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{x + 1} - \frac{\sin{\left(x \right)}}{\left(x + 1\right)^{2}}$$
1 1
------------------- - ---------------
/pi \ 2
(1 + x)*csc|-- - x| (1 + x) *csc(x)
\2 /
$$\frac{1}{\left(x + 1\right) \csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{\left(x + 1\right)^{2} \csc{\left(x \right)}}$$
1/((1 + x)*csc(pi/2 - x)) - 1/((1 + x)^2*csc(x))