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Simplificación de expresiones/ Descomposición en fracciones simples/ atan((4*x-4)/(2*sqrt(6)))/sqrt(6)

¿Cómo vas a descomponer esta atan((4*x-4)/(2*sqrt(6)))/sqrt(6) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /4*x - 4\
atan|-------|
    |    ___|
    \2*\/ 6 /
-------------
      ___    
    \/ 6
$$\frac{\operatorname{atan}{\left(\frac{4 x - 4}{2 \sqrt{6}} \right)}}{\sqrt{6}}$$ 
atan((4*x - 4)/((2*sqrt(6))))/sqrt(6)
Simplificación general [src] 
          /  ___         \
  ___     |\/ 6 *(-1 + x)|
\/ 6 *atan|--------------|
          \      3       /
--------------------------
            6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \left(x - 1\right)}{3} \right)}}{6}$$ 
sqrt(6)*atan(sqrt(6)*(-1 + x)/3)/6
Descomposición de una fracción [src] 
sqrt(6)*atan(-sqrt(6)/3 + x*sqrt(6)/3)/6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} - \frac{\sqrt{6}}{3} \right)}}{6}$$ 
          /    ___       ___\
  ___     |  \/ 6    x*\/ 6 |
\/ 6 *atan|- ----- + -------|
          \    3        3   /
-----------------------------
              6
Respuesta numérica [src] 
0.408248290463863*atan((4*x - 4)/((2*sqrt(6))))
0.408248290463863*atan((4*x - 4)/((2*sqrt(6))))
Unión de expresiones racionales [src] 
          /  ___         \
  ___     |\/ 6 *(-1 + x)|
\/ 6 *atan|--------------|
          \      3       /
--------------------------
            6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \left(x - 1\right)}{3} \right)}}{6}$$ 
sqrt(6)*atan(sqrt(6)*(-1 + x)/3)/6
Parte trigonométrica [src] 
          /  ___           \
  ___     |\/ 6 *(-4 + 4*x)|
\/ 6 *atan|----------------|
          \       12       /
----------------------------
             6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \left(4 x - 4\right)}{12} \right)}}{6}$$ 
sqrt(6)*atan(sqrt(6)*(-4 + 4*x)/12)/6
Denominador común [src] 
          /    ___       ___\
  ___     |  \/ 6    x*\/ 6 |
\/ 6 *atan|- ----- + -------|
          \    3        3   /
-----------------------------
              6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} - \frac{\sqrt{6}}{3} \right)}}{6}$$ 
sqrt(6)*atan(-sqrt(6)/3 + x*sqrt(6)/3)/6
Potencias [src] 
          /  ___           \
  ___     |\/ 6 *(-4 + 4*x)|
\/ 6 *atan|----------------|
          \       12       /
----------------------------
             6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \left(4 x - 4\right)}{12} \right)}}{6}$$ 
  ___     /  ___ /  1   x\\
\/ 6 *atan|\/ 6 *|- - + -||
          \      \  3   3//
---------------------------
             6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\sqrt{6} \left(\frac{x}{3} - \frac{1}{3}\right) \right)}}{6}$$ 
sqrt(6)*atan(sqrt(6)*(-1/3 + x/3))/6
Compilar la expresión [src] 
  ___     /4*x - 4\
\/ 6 *atan|-------|
          |    ___|
          \2*\/ 6 /
-------------------
         6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{4 x - 4}{2 \sqrt{6}} \right)}}{6}$$ 
sqrt(6)*atan((4*x - 4)/((2*sqrt(6))))/6
Combinatoria [src] 
          /    ___       ___\
  ___     |  \/ 6    x*\/ 6 |
\/ 6 *atan|- ----- + -------|
          \    3        3   /
-----------------------------
              6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} - \frac{\sqrt{6}}{3} \right)}}{6}$$ 
sqrt(6)*atan(-sqrt(6)/3 + x*sqrt(6)/3)/6
Abrimos la expresión [src] 
  ___     /  ___          \
\/ 6      |\/ 6 *(4*x - 4)|
-----*atan|---------------|
  6       \       12      /
$$\frac{\sqrt{6}}{6} \operatorname{atan}{\left(\frac{\sqrt{6} \left(4 x - 4\right)}{12} \right)}$$ 
(sqrt(6)/6)*atan(sqrt(6)*(4*x - 4)/12)
Denominador racional [src] 
          /  ___         \
  ___     |\/ 6 *(-1 + x)|
\/ 6 *atan|--------------|
          \      3       /
--------------------------
            6
$$\frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} \left(x - 1\right)}{3} \right)}}{6}$$ 
sqrt(6)*atan(sqrt(6)*(-1 + x)/3)/6
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