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¿Cómo vas a descomponer esta asinh((8*x-4)/(4*sqrt(6)))/2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
     /8*x - 4\
asinh|-------|
     |    ___|
     \4*\/ 6 /
--------------
      2       
$$\frac{\operatorname{asinh}{\left(\frac{8 x - 4}{4 \sqrt{6}} \right)}}{2}$$
asinh((8*x - 4)/((4*sqrt(6))))/2
Simplificación general [src]
     /  ___           \
     |\/ 6 *(-1 + 2*x)|
asinh|----------------|
     \       6        /
-----------------------
           2           
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{6} \left(2 x - 1\right)}{6} \right)}}{2}$$
asinh(sqrt(6)*(-1 + 2*x)/6)/2
Descomposición de una fracción [src]
asinh(-sqrt(6)/6 + x*sqrt(6)/3)/2
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{6} x}{3} - \frac{\sqrt{6}}{6} \right)}}{2}$$
     /    ___       ___\
     |  \/ 6    x*\/ 6 |
asinh|- ----- + -------|
     \    6        3   /
------------------------
           2            
Respuesta numérica [src]
0.5*asinh((8*x - 4)/((4*sqrt(6))))
0.5*asinh((8*x - 4)/((4*sqrt(6))))
Parte trigonométrica [src]
     /  ___           \
     |\/ 6 *(-4 + 8*x)|
asinh|----------------|
     \       24       /
-----------------------
           2           
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{6} \left(8 x - 4\right)}{24} \right)}}{2}$$
asinh(sqrt(6)*(-4 + 8*x)/24)/2
Denominador común [src]
     /    ___       ___\
     |  \/ 6    x*\/ 6 |
asinh|- ----- + -------|
     \    6        3   /
------------------------
           2            
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{6} x}{3} - \frac{\sqrt{6}}{6} \right)}}{2}$$
asinh(-sqrt(6)/6 + x*sqrt(6)/3)/2
Denominador racional [src]
     /  ___           \
     |\/ 6 *(-1 + 2*x)|
asinh|----------------|
     \       6        /
-----------------------
           2           
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{6} \left(2 x - 1\right)}{6} \right)}}{2}$$
asinh(sqrt(6)*(-1 + 2*x)/6)/2
Abrimos la expresión [src]
     /  ___          \
     |\/ 6 *(8*x - 4)|
asinh|---------------|
     \       24      /
----------------------
          2           
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{6} \left(8 x - 4\right)}{24} \right)}}{2}$$
asinh(sqrt(6)*(8*x - 4)/24)/2
Unión de expresiones racionales [src]
     /  ___           \
     |\/ 6 *(-1 + 2*x)|
asinh|----------------|
     \       6        /
-----------------------
           2           
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{6} \left(2 x - 1\right)}{6} \right)}}{2}$$
asinh(sqrt(6)*(-1 + 2*x)/6)/2
Potencias [src]
     /  ___ /  1   x\\
asinh|\/ 6 *|- - + -||
     \      \  6   3//
----------------------
          2           
$$\frac{\operatorname{asinh}{\left(\sqrt{6} \left(\frac{x}{3} - \frac{1}{6}\right) \right)}}{2}$$
     /  ___           \
     |\/ 6 *(-4 + 8*x)|
asinh|----------------|
     \       24       /
-----------------------
           2           
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{6} \left(8 x - 4\right)}{24} \right)}}{2}$$
asinh(sqrt(6)*(-4 + 8*x)/24)/2
Combinatoria [src]
     /    ___       ___\
     |  \/ 6    x*\/ 6 |
asinh|- ----- + -------|
     \    6        3   /
------------------------
           2            
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{6} x}{3} - \frac{\sqrt{6}}{6} \right)}}{2}$$
asinh(-sqrt(6)/6 + x*sqrt(6)/3)/2