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