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¿cómo vas a descomponer esta expresión en fracciones?:
45*x*y^2/(75*y^2)
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z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
Factorizar el polinomio:
y^7-2*y^5
-y^6+1
y*x^2+i*y^3/3
y^8-1
Descomponer al cuadrado:
y^4-9*y^2+10
y^4-9*y^2-15
y^4-9*y^2+4
y^4-9*y^2+2
Expresiones idénticas
atan(sin(dos *x)/(sqrt(cinco)*(uno +cos(dos *x))))/sqrt(cinco)
arco tangente de gente de ( seno de (2 multiplicar por x) dividir por ( raíz cuadrada de (5) multiplicar por (1 más coseno de (2 multiplicar por x)))) dividir por raíz cuadrada de (5)
arco tangente de gente de ( seno de (dos multiplicar por x) dividir por ( raíz cuadrada de (cinco) multiplicar por (uno más coseno de (dos multiplicar por x)))) dividir por raíz cuadrada de (cinco)
atan(sin(2*x)/(√(5)*(1+cos(2*x))))/√(5)
atan(sin(2x)/(sqrt(5)(1+cos(2x))))/sqrt(5)
atansin2x/sqrt51+cos2x/sqrt5
atan(sin(2*x) dividir por (sqrt(5)*(1+cos(2*x)))) dividir por sqrt(5)
Expresiones semejantes
atan(sin(2*x)/(sqrt(5)*(1-cos(2*x))))/sqrt(5)
arctan(sin(2*x)/(sqrt(5)*(1+cos(2*x))))/sqrt(5)
Expresiones con funciones
Arcotangente arctan
atan(3*pi/2)/(9*pi^2)
atan(x)/2+x/(2+2*x^2)
atan(5*x)/(x^3)-5/(2*x^2*(25*x^2+1))-125/(2+50*x^2)
atan(x/2)/16+x/(32+8*x^2)
atan(E^x)/(2*sqrt(x))+sqrt(x)*exp(x)/(1+exp(2*x))
Seno sin
sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3
sin(p/2+a)-cos(p+a)/((-sin(a-2*p)))
sin(2*a)/((2*tg(a)))
sin(2*x)/((19*sin(x)))
sin(7*n/(2-a))*(-7)
Raíz cuadrada sqrt
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+(b+2))
sqrt(16*x^2*(1-5/(16*x)))
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))
Coseno cos
cos(2*t)*t/(cos(t)+sin(t))-cos(t)
cos(4*x)/(8*(cos(4*x)^2)^(3/2))
cos(2*t)/(cos(t)+sin(t))
cos(2*x)*x/(sin(x)+cos(x))
cos(3п/2+а)1/(a*x-1)-1/(a*x+1)
Raíz cuadrada sqrt
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+(b+2))
sqrt(16*x^2*(1-5/(16*x)))
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))

Simplificación de expresiones/ Descomposición en fracciones simples/ atan(sin(2*x)/(sqrt(5)*(1+cos(2*x))))/sqrt(5)

¿Cómo vas a descomponer esta atan(sin(2x)/(sqrt(5)(1+cos(2*x))))/sqrt(5) expresión en fracciones?

Solución

Ha introducido [src]

    /      sin(2*x)      \
atan|--------------------|
    |  ___               |
    \\/ 5 *(1 + cos(2*x))/
--------------------------
            ___           
          \/ 5

$$\frac{\operatorname{atan}{\left(\frac{\sin{\left(2 x \right)}}{\sqrt{5} \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{\sqrt{5}}$$

atan(sin(2*x)/((sqrt(5)*(1 + cos(2*x)))))/sqrt(5)

Descomposición de una fracción [src]

sqrt(5)*atan(sin(2*x)/(sqrt(5) + sqrt(5)*cos(2*x)))/5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sin{\left(2 x \right)}}{\sqrt{5} \cos{\left(2 x \right)} + \sqrt{5}} \right)}}{5}$$

  ___     /       sin(2*x)       \
\/ 5 *atan|----------------------|
          |  ___     ___         |
          \\/ 5  + \/ 5 *cos(2*x)/
----------------------------------
                5

Simplificación general [src]

          /  ___       \
  ___     |\/ 5 *tan(x)|
\/ 5 *atan|------------|
          \     5      /
------------------------
           5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \tan{\left(x \right)}}{5} \right)}}{5}$$

sqrt(5)*atan(sqrt(5)*tan(x)/5)/5

Respuesta numérica [src]

0.447213595499958*atan(sin(2*x)/((sqrt(5)*(1 + cos(2*x)))))

0.447213595499958*atan(sin(2*x)/((sqrt(5)*(1 + cos(2*x)))))

Denominador racional [src]

          /   ___          \
  ___     | \/ 5 *sin(2*x) |
\/ 5 *atan|----------------|
          \5*(1 + cos(2*x))/
----------------------------
             5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sin{\left(2 x \right)}}{5 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{5}$$

sqrt(5)*atan(sqrt(5)*sin(2*x)/(5*(1 + cos(2*x))))/5

Denominador común [src]

          /   ___          \
  ___     | \/ 5 *sin(2*x) |
\/ 5 *atan|----------------|
          \5*(1 + cos(2*x))/
----------------------------
             5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sin{\left(2 x \right)}}{5 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{5}$$

sqrt(5)*atan(sqrt(5)*sin(2*x)/(5*(1 + cos(2*x))))/5

Potencias [src]

           /    ___ /   -2*I*x    2*I*x\\ 
   ___     |I*\/ 5 *\- e       + e     /| 
-\/ 5 *atan|----------------------------| 
           |    /     -2*I*x    2*I*x\  | 
           |    |    e         e     |  | 
           | 10*|1 + ------- + ------|  | 
           \    \       2        2   /  / 
------------------------------------------
                    5

$$- \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} i \left(e^{2 i x} - e^{- 2 i x}\right)}{10 \left(\frac{e^{2 i x}}{2} + 1 + \frac{e^{- 2 i x}}{2}\right)} \right)}}{5}$$

          /   ___          \
  ___     | \/ 5 *sin(2*x) |
\/ 5 *atan|----------------|
          \5*(1 + cos(2*x))/
----------------------------
             5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sin{\left(2 x \right)}}{5 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{5}$$

sqrt(5)*atan(sqrt(5)*sin(2*x)/(5*(1 + cos(2*x))))/5

Combinatoria [src]

          /   ___          \
  ___     | \/ 5 *sin(2*x) |
\/ 5 *atan|----------------|
          \5*(1 + cos(2*x))/
----------------------------
             5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sin{\left(2 x \right)}}{5 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{5}$$

sqrt(5)*atan(sqrt(5)*sin(2*x)/(5*(1 + cos(2*x))))/5

Unión de expresiones racionales [src]

          /   ___          \
  ___     | \/ 5 *sin(2*x) |
\/ 5 *atan|----------------|
          \5*(1 + cos(2*x))/
----------------------------
             5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sin{\left(2 x \right)}}{5 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{5}$$

sqrt(5)*atan(sqrt(5)*sin(2*x)/(5*(1 + cos(2*x))))/5

Abrimos la expresión [src]

  ___     /   ___          \
\/ 5      | \/ 5 *sin(2*x) |
-----*atan|----------------|
  5       \5*(1 + cos(2*x))/

$$\frac{\sqrt{5}}{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sin{\left(2 x \right)}}{5 \left(\cos{\left(2 x \right)} + 1\right)} \right)}$$

          /  ___       \
  ___     |\/ 5 *sin(x)|
\/ 5 *atan|------------|
          \  5*cos(x)  /
------------------------
           5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sin{\left(x \right)}}{5 \cos{\left(x \right)}} \right)}}{5}$$

sqrt(5)*atan(sqrt(5)*sin(x)/(5*cos(x)))/5

Compilar la expresión [src]

  ___     /      sin(2*x)      \
\/ 5 *atan|--------------------|
          |  ___               |
          \\/ 5 *(1 + cos(2*x))/
--------------------------------
               5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sin{\left(2 x \right)}}{\sqrt{5} \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{5}$$

sqrt(5)*atan(sin(2*x)/((sqrt(5)*(1 + cos(2*x)))))/5

Parte trigonométrica [src]

          /      ___            \
  ___     |    \/ 5 *sin(2*x)   |
\/ 5 *atan|---------------------|
          |  /       /pi      \\|
          |5*|1 + sin|-- + 2*x|||
          \  \       \2       ///
---------------------------------
                5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sin{\left(2 x \right)}}{5 \left(\sin{\left(2 x + \frac{\pi}{2} \right)} + 1\right)} \right)}}{5}$$

          /              ___                 \
  ___     |          2*\/ 5 *cot(x)          |
\/ 5 *atan|----------------------------------|
          |                /            2   \|
          |  /       2   \ |    -1 + cot (x)||
          |5*\1 + cot (x)/*|1 + ------------||
          |                |           2    ||
          \                \    1 + cot (x) //
----------------------------------------------
                      5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5} \cot{\left(x \right)}}{5 \left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)} \right)}}{5}$$

          /   ___  \
  ___     | \/ 5   |
\/ 5 *atan|--------|
          \5*cot(x)/
--------------------
         5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5 \cot{\left(x \right)}} \right)}}{5}$$

          /   ___       \
  ___     | \/ 5 *sec(x)|
\/ 5 *atan|-------------|
          |     /    pi\|
          |5*sec|x - --||
          \     \    2 //
-------------------------
            5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sec{\left(x \right)}}{5 \sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{5}$$

          /              ___             \
  ___     |            \/ 5              |
\/ 5 *atan|------------------------------|
          |  /       1    \    /      pi\|
          |5*|1 + --------|*sec|2*x - --||
          \  \    sec(2*x)/    \      2 //
------------------------------------------
                    5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5 \left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}} \right)}}{5}$$

          /            ___          \
  ___     |          \/ 5           |
\/ 5 *atan|-------------------------|
          |  /       1    \         |
          |5*|1 + --------|*csc(2*x)|
          \  \    sec(2*x)/         /
-------------------------------------
                  5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5 \left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \csc{\left(2 x \right)}} \right)}}{5}$$

          /              ___             \
  ___     |            \/ 5              |
\/ 5 *atan|------------------------------|
          |  /          1      \         |
          |5*|1 + -------------|*csc(2*x)|
          |  |       /pi      \|         |
          |  |    csc|-- - 2*x||         |
          \  \       \2       //         /
------------------------------------------
                    5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5 \left(1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc{\left(2 x \right)}} \right)}}{5}$$

          /  ___       \
  ___     |\/ 5 *tan(x)|
\/ 5 *atan|------------|
          \     5      /
------------------------
           5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \tan{\left(x \right)}}{5} \right)}}{5}$$

          /  ___    /      pi\\
          |\/ 5 *cos|2*x - --||
  ___     |         \      2 /|
\/ 5 *atan|-------------------|
          \  5*(1 + cos(2*x)) /
-------------------------------
               5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \cos{\left(2 x - \frac{\pi}{2} \right)}}{5 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{5}$$

          /    ___    2   \
  ___     |2*\/ 5 *sin (x)|
\/ 5 *atan|---------------|
          \   5*sin(2*x)  /
---------------------------
             5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5} \sin^{2}{\left(x \right)}}{5 \sin{\left(2 x \right)}} \right)}}{5}$$

          /  ___    /pi    \\
          |\/ 5 *csc|-- - x||
  ___     |         \2     /|
\/ 5 *atan|-----------------|
          \     5*csc(x)    /
-----------------------------
              5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \csc{\left(- x + \frac{\pi}{2} \right)}}{5 \csc{\left(x \right)}} \right)}}{5}$$

          /              ___                \
  ___     |          2*\/ 5 *tan(x)         |
\/ 5 *atan|---------------------------------|
          |                /           2   \|
          |  /       2   \ |    1 - tan (x)||
          |5*\1 + tan (x)/*|1 + -----------||
          |                |           2   ||
          \                \    1 + tan (x)//
---------------------------------------------
                      5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5} \tan{\left(x \right)}}{5 \left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)} \right)}}{5}$$

          /   ___          \
  ___     | \/ 5 *sin(2*x) |
\/ 5 *atan|----------------|
          \5*(1 + cos(2*x))/
----------------------------
             5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \sin{\left(2 x \right)}}{5 \left(\cos{\left(2 x \right)} + 1\right)} \right)}}{5}$$

          /  ___    /    pi\\
          |\/ 5 *cos|x - --||
  ___     |         \    2 /|
\/ 5 *atan|-----------------|
          \     5*cos(x)    /
-----------------------------
              5

$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \cos{\left(x - \frac{\pi}{2} \right)}}{5 \cos{\left(x \right)}} \right)}}{5}$$

sqrt(5)*atan(sqrt(5)*cos(x - pi/2)/(5*cos(x)))/5

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta atan(sin(2*x)/(sqrt(5)*(1+cos(2*x))))/sqrt(5) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta atan(sin(2x)/(sqrt(5)(1+cos(2*x))))/sqrt(5) expresión en fracciones?