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¿cómo vas a descomponer esta expresión en fracciones?:
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Expresiones semejantes
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Expresiones con funciones
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Raíz cuadrada sqrt
sqrt((x^2+10^8)/(1+25*x^2))
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sqrt(x)/(x^2+y^2)+sqrt(y)/(x^2-y^2)
Raíz cuadrada sqrt
sqrt((x^2+10^8)/(1+25*x^2))
sqrt(w^2*(-t^2)/(1+t^2*w^2)+(t*w/(1+t^2*w^2))^2)
sqrt((49)/(169^x^196))
sqrt(2)*(4-3*(1+x-2*x^2)/(1+2*x)^2-2*(-1+4*x)/(1+2*x))/(6*sqrt(1+2*x))
sqrt(x)/(x^2+y^2)+sqrt(y)/(x^2-y^2)

Simplificación de expresiones/ Descomposición en fracciones simples/ atan(((2*sin(x))/(1+cos(x))+3)/sqrt(3))/sqrt(3)

¿Cómo vas a descomponer esta atan(((2*sin(x))/(1+cos(x))+3)/sqrt(3))/sqrt(3) expresión en fracciones?

Solución

Ha introducido [src]

    / 2*sin(x)     \
    |---------- + 3|
    |1 + cos(x)    |
atan|--------------|
    |      ___     |
    \    \/ 3      /
--------------------
         ___        
       \/ 3

$$\frac{\operatorname{atan}{\left(\frac{3 + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{\sqrt{3}} \right)}}{\sqrt{3}}$$

atan(((2*sin(x))/(1 + cos(x)) + 3)/sqrt(3))/sqrt(3)

Descomposición de una fracción [src]

sqrt(3)*atan(3*sqrt(3)/3 + 2*(sqrt(3)/3)*sin(x)/(1 + cos(x)))/3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{3 \sqrt{3}}{3} + \frac{2 \frac{\sqrt{3}}{3} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)}}{3}$$

          /              ___       \
          |            \/ 3        |
          |    ___   2*-----*sin(x)|
  ___     |3*\/ 3        3         |
\/ 3 *atan|------- + --------------|
          \   3        1 + cos(x)  /
------------------------------------
                 3

Simplificación general [src]

          /  ___ /    2*sin(x)         \\
          |\/ 3 *|1 + -------- + cos(x)||
  ___     |      \       3             /|
\/ 3 *atan|-----------------------------|
          \          1 + cos(x)         /
-----------------------------------------
                    3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(\frac{2 \sin{\left(x \right)}}{3} + \cos{\left(x \right)} + 1\right)}{\cos{\left(x \right)} + 1} \right)}}{3}$$

sqrt(3)*atan(sqrt(3)*(1 + 2*sin(x)/3 + cos(x))/(1 + cos(x)))/3

Potencias [src]

          /  ___ /     2*sin(x) \\
          |\/ 3 *|3 + ----------||
  ___     |      \    1 + cos(x)/|
\/ 3 *atan|----------------------|
          \          3           /
----------------------------------
                3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(3 + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)}{3} \right)}}{3}$$

  ___     /  ___ /       2*sin(x)   \\
\/ 3 *atan|\/ 3 *|1 + --------------||
          \      \    3*(1 + cos(x))//
--------------------------------------
                  3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(1 + \frac{2 \sin{\left(x \right)}}{3 \left(\cos{\left(x \right)} + 1\right)}\right) \right)}}{3}$$

          /      /      /   -I*x    I*x\\\
          |  ___ |    I*\- e     + e   /||
          |\/ 3 *|3 - ------------------||
          |      |          I*x    -I*x ||
          |      |         e      e     ||
          |      |     1 + ---- + ----- ||
  ___     |      \          2       2   /|
\/ 3 *atan|------------------------------|
          \              3               /
------------------------------------------
                    3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}} + 3\right)}{3} \right)}}{3}$$

sqrt(3)*atan(sqrt(3)*(3 - i*(-exp(-i*x) + exp(i*x))/(1 + exp(i*x)/2 + exp(-i*x)/2))/3)/3

Unión de expresiones racionales [src]

          /  ___                          \
  ___     |\/ 3 *(3 + 2*sin(x) + 3*cos(x))|
\/ 3 *atan|-------------------------------|
          \         3*(1 + cos(x))        /
-------------------------------------------
                     3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)} + 3\right)}{3 \left(\cos{\left(x \right)} + 1\right)} \right)}}{3}$$

sqrt(3)*atan(sqrt(3)*(3 + 2*sin(x) + 3*cos(x))/(3*(1 + cos(x))))/3

Denominador común [src]

          /            ___       \
  ___     |  ___   2*\/ 3 *sin(x)|
\/ 3 *atan|\/ 3  + --------------|
          \        3*(1 + cos(x))/
----------------------------------
                3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} + \frac{2 \sqrt{3} \sin{\left(x \right)}}{3 \left(\cos{\left(x \right)} + 1\right)} \right)}}{3}$$

sqrt(3)*atan(sqrt(3) + 2*sqrt(3)*sin(x)/(3*(1 + cos(x))))/3

Abrimos la expresión [src]

          /              ___       \
          |            \/ 3        |
  ___     |    ___   2*-----*sin(x)|
\/ 3      |3*\/ 3        3         |
-----*atan|------- + --------------|
  3       \   3        1 + cos(x)  /

$$\frac{\sqrt{3}}{3} \operatorname{atan}{\left(\frac{3 \sqrt{3}}{3} + \frac{2 \frac{\sqrt{3}}{3} \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)}$$

(sqrt(3)/3)*atan(3*sqrt(3)/3 + 2*(sqrt(3)/3)*sin(x)/(1 + cos(x)))

Compilar la expresión [src]

          / 2*sin(x)     \
          |---------- + 3|
  ___     |1 + cos(x)    |
\/ 3 *atan|--------------|
          |      ___     |
          \    \/ 3      /
--------------------------
            3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{3 + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{\sqrt{3}} \right)}}{3}$$

sqrt(3)*atan(((2*sin(x))/(1 + cos(x)) + 3)/sqrt(3))/3

Respuesta numérica [src]

0.577350269189626*atan(((2*sin(x))/(1 + cos(x)) + 3)/sqrt(3))

0.577350269189626*atan(((2*sin(x))/(1 + cos(x)) + 3)/sqrt(3))

Parte trigonométrica [src]

          /  ___ /     2*sin(x) \\
          |\/ 3 *|3 + ----------||
  ___     |      \    1 + cos(x)/|
\/ 3 *atan|----------------------|
          \          3           /
----------------------------------
                3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(3 + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)}{3} \right)}}{3}$$

          /      /         /    pi\\\
          |      |    2*cos|x - --|||
          |  ___ |         \    2 /||
          |\/ 3 *|3 + -------------||
  ___     |      \      1 + cos(x) /|
\/ 3 *atan|-------------------------|
          \            3            /
-------------------------------------
                  3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(3 + \frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1}\right)}{3} \right)}}{3}$$

  ___     /  ___ /       2*sin(x)   \\
\/ 3 *atan|\/ 3 *|1 + --------------||
          \      \    3*(1 + cos(x))//
--------------------------------------
                  3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(1 + \frac{2 \sin{\left(x \right)}}{3 \left(\cos{\left(x \right)} + 1\right)}\right) \right)}}{3}$$

          /      /         /    pi\ \\
          |      |    2*cos|x - --| ||
  ___     |  ___ |         \    2 / ||
\/ 3 *atan|\/ 3 *|1 + --------------||
          \      \    3*(1 + cos(x))//
--------------------------------------
                  3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(1 + \frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3 \left(\cos{\left(x \right)} + 1\right)}\right) \right)}}{3}$$

          /      /                     /x\           \\
          |      |                4*tan|-|           ||
          |  ___ |                     \2/           ||
          |\/ 3 *|3 + -------------------------------||
          |      |                  /           2/x\\||
          |      |                  |    1 - tan |-||||
          |      |    /       2/x\\ |            \2/|||
          |      |    |1 + tan |-||*|1 + -----------|||
          |      |    \        \2// |           2/x\|||
          |      |                  |    1 + tan |-||||
  ___     |      \                  \            \2///|
\/ 3 *atan|-------------------------------------------|
          \                     3                     /
-------------------------------------------------------
                           3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(3 + \frac{4 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right)}{3} \right)}}{3}$$

          /      /                      /x\            \\
          |      |                 4*tan|-|            ||
  ___     |  ___ |                      \2/            ||
\/ 3 *atan|\/ 3 *|1 + ---------------------------------||
          |      |                    /           2/x\\||
          |      |                    |    1 - tan |-||||
          |      |      /       2/x\\ |            \2/|||
          |      |    3*|1 + tan |-||*|1 + -----------|||
          |      |      \        \2// |           2/x\|||
          |      |                    |    1 + tan |-||||
          \      \                    \            \2////
---------------------------------------------------------
                            3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(1 + \frac{4 \tan{\left(\frac{x}{2} \right)}}{3 \left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right) \right)}}{3}$$

          /  ___ /               2            \\
          |\/ 3 *|3 + ------------------------||
          |      |    /         1     \       ||
          |      |    |1 + -----------|*csc(x)||
          |      |    |       /pi    \|       ||
          |      |    |    csc|-- - x||       ||
  ___     |      \    \       \2     //       /|
\/ 3 *atan|------------------------------------|
          \                 3                  /
------------------------------------------------
                       3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(3 + \frac{2}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}\right)}{3} \right)}}{3}$$

          /  ___ /        2*sin(x)   \\
          |\/ 3 *|3 + ---------------||
          |      |           /    pi\||
          |      |    1 + sin|x + --|||
  ___     |      \           \    2 //|
\/ 3 *atan|---------------------------|
          \             3             /
---------------------------------------
                   3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(3 + \frac{2 \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1}\right)}{3} \right)}}{3}$$

          /  ___ /               2            \\
          |\/ 3 *|3 + ------------------------||
          |      |    /      1   \    /    pi\||
          |      |    |1 + ------|*sec|x - --|||
  ___     |      \    \    sec(x)/    \    2 //|
\/ 3 *atan|------------------------------------|
          \                 3                  /
------------------------------------------------
                       3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(3 + \frac{2}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}\right)}{3} \right)}}{3}$$

          /      /                     /x\            \\
          |      |                4*cot|-|            ||
          |  ___ |                     \2/            ||
          |\/ 3 *|3 + --------------------------------||
          |      |                  /            2/x\\||
          |      |                  |    -1 + cot |-||||
          |      |    /       2/x\\ |             \2/|||
          |      |    |1 + cot |-||*|1 + ------------|||
          |      |    \        \2// |           2/x\ |||
          |      |                  |    1 + cot |-| |||
  ___     |      \                  \            \2/ //|
\/ 3 *atan|--------------------------------------------|
          \                     3                      /
--------------------------------------------------------
                           3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(3 + \frac{4 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right)}{3} \right)}}{3}$$

  ___     /  ___ /                2             \\
\/ 3 *atan|\/ 3 *|1 + --------------------------||
          |      |      /         1     \       ||
          |      |    3*|1 + -----------|*csc(x)||
          |      |      |       /pi    \|       ||
          |      |      |    csc|-- - x||       ||
          \      \      \       \2     //       //
--------------------------------------------------
                        3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(1 + \frac{2}{3 \left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}\right) \right)}}{3}$$

  ___     /  ___ /          2*sin(x)     \\
\/ 3 *atan|\/ 3 *|1 + -------------------||
          |      |      /       /    pi\\||
          |      |    3*|1 + sin|x + --||||
          \      \      \       \    2 ////
-------------------------------------------
                     3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(1 + \frac{2 \sin{\left(x \right)}}{3 \left(\sin{\left(x + \frac{\pi}{2} \right)} + 1\right)}\right) \right)}}{3}$$

          /      /                      /x\             \\
          |      |                 4*cot|-|             ||
  ___     |  ___ |                      \2/             ||
\/ 3 *atan|\/ 3 *|1 + ----------------------------------||
          |      |                    /            2/x\\||
          |      |                    |    -1 + cot |-||||
          |      |      /       2/x\\ |             \2/|||
          |      |    3*|1 + cot |-||*|1 + ------------|||
          |      |      \        \2// |           2/x\ |||
          |      |                    |    1 + cot |-| |||
          \      \                    \            \2/ ///
----------------------------------------------------------
                            3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(1 + \frac{4 \cot{\left(\frac{x}{2} \right)}}{3 \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right) \right)}}{3}$$

  ___     /  ___ /                2             \\
\/ 3 *atan|\/ 3 *|1 + --------------------------||
          |      |      /      1   \    /    pi\||
          |      |    3*|1 + ------|*sec|x - --|||
          \      \      \    sec(x)/    \    2 ///
--------------------------------------------------
                        3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(1 + \frac{2}{3 \left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}\right) \right)}}{3}$$

          /  ___ /             2         \\
          |\/ 3 *|3 + -------------------||
          |      |    /      1   \       ||
          |      |    |1 + ------|*csc(x)||
  ___     |      \    \    sec(x)/       /|
\/ 3 *atan|-------------------------------|
          \               3               /
-------------------------------------------
                     3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(3 + \frac{2}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}}\right)}{3} \right)}}{3}$$

sqrt(3)*atan(sqrt(3)*(3 + 2/((1 + 1/sec(x))*csc(x)))/3)/3

Combinatoria [src]

          /            ___       \
  ___     |  ___   2*\/ 3 *sin(x)|
\/ 3 *atan|\/ 3  + --------------|
          \        3*(1 + cos(x))/
----------------------------------
                3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} + \frac{2 \sqrt{3} \sin{\left(x \right)}}{3 \left(\cos{\left(x \right)} + 1\right)} \right)}}{3}$$

sqrt(3)*atan(sqrt(3) + 2*sqrt(3)*sin(x)/(3*(1 + cos(x))))/3

Denominador racional [src]

          /  ___                          \
  ___     |\/ 3 *(3 + 2*sin(x) + 3*cos(x))|
\/ 3 *atan|-------------------------------|
          \         3*(1 + cos(x))        /
-------------------------------------------
                     3

$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 \sin{\left(x \right)} + 3 \cos{\left(x \right)} + 3\right)}{3 \left(\cos{\left(x \right)} + 1\right)} \right)}}{3}$$

sqrt(3)*atan(sqrt(3)*(3 + 2*sin(x) + 3*cos(x))/(3*(1 + cos(x))))/3

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta atan(((2*sin(x))/(1+cos(x))+3)/sqrt(3))/sqrt(3) expresión en fracciones?

Solución