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Simplificación de expresiones/ Descomposición en fracciones simples/ atan((2*x+4)/(2*sqrt(3)))/sqrt(3)

¿Cómo vas a descomponer esta atan((2*x+4)/(2*sqrt(3)))/sqrt(3) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /2*x + 4\
atan|-------|
    |    ___|
    \2*\/ 3 /
-------------
      ___    
    \/ 3
$$\frac{\operatorname{atan}{\left(\frac{2 x + 4}{2 \sqrt{3}} \right)}}{\sqrt{3}}$$ 
atan((2*x + 4)/((2*sqrt(3))))/sqrt(3)
Simplificación general [src] 
          /  ___        \
  ___     |\/ 3 *(2 + x)|
\/ 3 *atan|-------------|
          \      3      /
-------------------------
            3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 2\right)}{3} \right)}}{3}$$ 
sqrt(3)*atan(sqrt(3)*(2 + x)/3)/3
Descomposición de una fracción [src] 
sqrt(3)*atan(2*sqrt(3)/3 + x*sqrt(3)/3)/3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} + \frac{2 \sqrt{3}}{3} \right)}}{3}$$ 
          /    ___       ___\
  ___     |2*\/ 3    x*\/ 3 |
\/ 3 *atan|------- + -------|
          \   3         3   /
-----------------------------
              3
Respuesta numérica [src] 
0.577350269189626*atan((2*x + 4)/((2*sqrt(3))))
0.577350269189626*atan((2*x + 4)/((2*sqrt(3))))
Denominador racional [src] 
          /  ___        \
  ___     |\/ 3 *(2 + x)|
\/ 3 *atan|-------------|
          \      3      /
-------------------------
            3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 2\right)}{3} \right)}}{3}$$ 
sqrt(3)*atan(sqrt(3)*(2 + x)/3)/3
Denominador común [src] 
          /    ___       ___\
  ___     |2*\/ 3    x*\/ 3 |
\/ 3 *atan|------- + -------|
          \   3         3   /
-----------------------------
              3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} + \frac{2 \sqrt{3}}{3} \right)}}{3}$$ 
sqrt(3)*atan(2*sqrt(3)/3 + x*sqrt(3)/3)/3
Compilar la expresión [src] 
  ___     /2*x + 4\
\/ 3 *atan|-------|
          |    ___|
          \2*\/ 3 /
-------------------
         3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 x + 4}{2 \sqrt{3}} \right)}}{3}$$ 
sqrt(3)*atan((2*x + 4)/((2*sqrt(3))))/3
Combinatoria [src] 
          /    ___       ___\
  ___     |2*\/ 3    x*\/ 3 |
\/ 3 *atan|------- + -------|
          \   3         3   /
-----------------------------
              3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} + \frac{2 \sqrt{3}}{3} \right)}}{3}$$ 
sqrt(3)*atan(2*sqrt(3)/3 + x*sqrt(3)/3)/3
Parte trigonométrica [src] 
          /  ___          \
  ___     |\/ 3 *(4 + 2*x)|
\/ 3 *atan|---------------|
          \       6       /
---------------------------
             3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 4\right)}{6} \right)}}{3}$$ 
sqrt(3)*atan(sqrt(3)*(4 + 2*x)/6)/3
Potencias [src] 
          /  ___          \
  ___     |\/ 3 *(4 + 2*x)|
\/ 3 *atan|---------------|
          \       6       /
---------------------------
             3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 4\right)}{6} \right)}}{3}$$ 
  ___     /  ___ /2   x\\
\/ 3 *atan|\/ 3 *|- + -||
          \      \3   3//
-------------------------
            3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(\frac{x}{3} + \frac{2}{3}\right) \right)}}{3}$$ 
sqrt(3)*atan(sqrt(3)*(2/3 + x/3))/3
Unión de expresiones racionales [src] 
          /  ___        \
  ___     |\/ 3 *(2 + x)|
\/ 3 *atan|-------------|
          \      3      /
-------------------------
            3
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 2\right)}{3} \right)}}{3}$$ 
sqrt(3)*atan(sqrt(3)*(2 + x)/3)/3
Abrimos la expresión [src] 
  ___     /  ___          \
\/ 3      |\/ 3 *(2*x + 4)|
-----*atan|---------------|
  3       \       6       /
$$\frac{\sqrt{3}}{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 4\right)}{6} \right)}$$ 
(sqrt(3)/3)*atan(sqrt(3)*(2*x + 4)/6)
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