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Simplificación de expresiones/ Descomposición en fracciones simples/ asinh((6*x+6)/(2*sqrt(3)))/sqrt(3)

¿Cómo vas a descomponer esta asinh((6*x+6)/(2*sqrt(3)))/sqrt(3) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     /6*x + 6\
asinh|-------|
     |    ___|
     \2*\/ 3 /
--------------
      ___     
    \/ 3
$$\frac{\operatorname{asinh}{\left(\frac{6 x + 6}{2 \sqrt{3}} \right)}}{\sqrt{3}}$$ 
asinh((6*x + 6)/((2*sqrt(3))))/sqrt(3)
Simplificación general [src] 
  ___      /  ___        \
\/ 3 *asinh\\/ 3 *(1 + x)/
--------------------------
            3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} \left(x + 1\right) \right)}}{3}$$ 
sqrt(3)*asinh(sqrt(3)*(1 + x))/3
Descomposición de una fracción [src] 
sqrt(3)*asinh(sqrt(3) + x*sqrt(3))/3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x + \sqrt{3} \right)}}{3}$$ 
  ___      /  ___       ___\
\/ 3 *asinh\\/ 3  + x*\/ 3 /
----------------------------
             3
Respuesta numérica [src] 
0.577350269189626*asinh((6*x + 6)/((2*sqrt(3))))
0.577350269189626*asinh((6*x + 6)/((2*sqrt(3))))
Abrimos la expresión [src] 
  ___      /  ___          \
\/ 3       |\/ 3 *(6*x + 6)|
-----*asinh|---------------|
  3        \       6       /
$$\frac{\sqrt{3}}{3} \operatorname{asinh}{\left(\frac{\sqrt{3} \left(6 x + 6\right)}{6} \right)}$$ 
(sqrt(3)/3)*asinh(sqrt(3)*(6*x + 6)/6)
Denominador común [src] 
  ___      /  ___       ___\
\/ 3 *asinh\\/ 3  + x*\/ 3 /
----------------------------
             3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x + \sqrt{3} \right)}}{3}$$ 
sqrt(3)*asinh(sqrt(3) + x*sqrt(3))/3
Potencias [src] 
           /  ___          \
  ___      |\/ 3 *(6 + 6*x)|
\/ 3 *asinh|---------------|
           \       6       /
----------------------------
             3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{3} \left(6 x + 6\right)}{6} \right)}}{3}$$ 
  ___      /  ___        \
\/ 3 *asinh\\/ 3 *(1 + x)/
--------------------------
            3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} \left(x + 1\right) \right)}}{3}$$ 
sqrt(3)*asinh(sqrt(3)*(1 + x))/3
Parte trigonométrica [src] 
           /  ___          \
  ___      |\/ 3 *(6 + 6*x)|
\/ 3 *asinh|---------------|
           \       6       /
----------------------------
             3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{3} \left(6 x + 6\right)}{6} \right)}}{3}$$ 
sqrt(3)*asinh(sqrt(3)*(6 + 6*x)/6)/3
Denominador racional [src] 
  ___      /  ___        \
\/ 3 *asinh\\/ 3 *(1 + x)/
--------------------------
            3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} \left(x + 1\right) \right)}}{3}$$ 
sqrt(3)*asinh(sqrt(3)*(1 + x))/3
Unión de expresiones racionales [src] 
  ___      /  ___        \
\/ 3 *asinh\\/ 3 *(1 + x)/
--------------------------
            3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} \left(x + 1\right) \right)}}{3}$$ 
sqrt(3)*asinh(sqrt(3)*(1 + x))/3
Combinatoria [src] 
  ___      /  ___       ___\
\/ 3 *asinh\\/ 3  + x*\/ 3 /
----------------------------
             3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x + \sqrt{3} \right)}}{3}$$ 
sqrt(3)*asinh(sqrt(3) + x*sqrt(3))/3
Compilar la expresión [src] 
  ___      /6*x + 6\
\/ 3 *asinh|-------|
           |    ___|
           \2*\/ 3 /
--------------------
         3
$$\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{6 x + 6}{2 \sqrt{3}} \right)}}{3}$$ 
sqrt(3)*asinh((6*x + 6)/((2*sqrt(3))))/3
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