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Simplificación de expresiones/ Descomposición en fracciones simples/ asinh(x/(sqrt(2)*|x+1|)-sqrt(2)/|x+1|)/sqrt(3)

¿Cómo vas a descomponer esta asinh(x/(sqrt(2)*|x+1|)-sqrt(2)/|x+1|)/sqrt(3) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     /                   ___ \
     |      x          \/ 2  |
asinh|------------- - -------|
     |  ___           |x + 1||
     \\/ 2 *|x + 1|          /
------------------------------
              ___             
            \/ 3
asinh⁡(x2∣x+1∣−2∣x+1∣)3\frac{\operatorname{asinh}{\left(\frac{x}{\sqrt{2} \left|{x + 1}\right|} - \frac{\sqrt{2}}{\left|{x + 1}\right|} \right)}}{\sqrt{3}} 
asinh(x/((sqrt(2)*|x + 1|)) - sqrt(2)/|x + 1|)/sqrt(3)
Simplificación general [src] 
           /  ___         \
  ___      |\/ 2 *(-2 + x)|
\/ 3 *asinh|--------------|
           \  2*|1 + x|   /
---------------------------
             3
3asinh⁡(2(x−2)2∣x+1∣)3\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{2} \left(x - 2\right)}{2 \left|{x + 1}\right|} \right)}}{3} 
sqrt(3)*asinh(sqrt(2)*(-2 + x)/(2*|1 + x|))/3
Descomposición de una fracción [src] 
sqrt(3)*asinh(-sqrt(2)/|x + 1| + x*sqrt(2)/(2*|x + 1|))/3
3asinh⁡(2x2∣x+1∣−2∣x+1∣)3\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{x + 1}\right|} - \frac{\sqrt{2}}{\left|{x + 1}\right|} \right)}}{3} 
           /     ___         ___ \
  ___      |   \/ 2      x*\/ 2  |
\/ 3 *asinh|- ------- + ---------|
           \  |x + 1|   2*|x + 1|/
----------------------------------
                3
Respuesta numérica [src] 
0.577350269189626*asinh(x/((sqrt(2)*|x + 1|)) - sqrt(2)/|x + 1|)
0.577350269189626*asinh(x/((sqrt(2)*|x + 1|)) - sqrt(2)/|x + 1|)
Combinatoria [src] 
           /     ___         ___ \
  ___      |   \/ 2      x*\/ 2  |
\/ 3 *asinh|- ------- + ---------|
           \  |1 + x|   2*|1 + x|/
----------------------------------
                3
3asinh⁡(2x2∣x+1∣−2∣x+1∣)3\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{x + 1}\right|} - \frac{\sqrt{2}}{\left|{x + 1}\right|} \right)}}{3} 
sqrt(3)*asinh(-sqrt(2)/|1 + x| + x*sqrt(2)/(2*|1 + x|))/3
Unión de expresiones racionales [src] 
           /  ___         \
  ___      |\/ 2 *(-2 + x)|
\/ 3 *asinh|--------------|
           \  2*|1 + x|   /
---------------------------
             3
3asinh⁡(2(x−2)2∣x+1∣)3\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{2} \left(x - 2\right)}{2 \left|{x + 1}\right|} \right)}}{3} 
sqrt(3)*asinh(sqrt(2)*(-2 + x)/(2*|1 + x|))/3
Potencias [src] 
           /     ___         ___ \
  ___      |   \/ 2      x*\/ 2  |
\/ 3 *asinh|- ------- + ---------|
           \  |1 + x|   2*|1 + x|/
----------------------------------
                3
3asinh⁡(2x2∣x+1∣−2∣x+1∣)3\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{x + 1}\right|} - \frac{\sqrt{2}}{\left|{x + 1}\right|} \right)}}{3} 
sqrt(3)*asinh(-sqrt(2)/|1 + x| + x*sqrt(2)/(2*|1 + x|))/3
Parte trigonométrica [src] 
           /     ___         ___ \
  ___      |   \/ 2      x*\/ 2  |
\/ 3 *asinh|- ------- + ---------|
           \  |1 + x|   2*|1 + x|/
----------------------------------
                3
3asinh⁡(2x2∣x+1∣−2∣x+1∣)3\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{x + 1}\right|} - \frac{\sqrt{2}}{\left|{x + 1}\right|} \right)}}{3} 
sqrt(3)*asinh(-sqrt(2)/|1 + x| + x*sqrt(2)/(2*|1 + x|))/3
Compilar la expresión [src] 
           /                   ___ \
  ___      |      x          \/ 2  |
\/ 3 *asinh|------------- - -------|
           |  ___           |x + 1||
           \\/ 2 *|x + 1|          /
------------------------------------
                 3
3asinh⁡(x2∣x+1∣−2∣x+1∣)3\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{x}{\sqrt{2} \left|{x + 1}\right|} - \frac{\sqrt{2}}{\left|{x + 1}\right|} \right)}}{3} 
sqrt(3)*asinh(x/((sqrt(2)*|x + 1|)) - sqrt(2)/|x + 1|)/3
Abrimos la expresión [src] 
  ___      /     ___         ___ \
\/ 3       |   \/ 2      x*\/ 2  |
-----*asinh|- ------- + ---------|
  3        \  |x + 1|   2*|x + 1|/
33asinh⁡(2x2∣x+1∣−2∣x+1∣)\frac{\sqrt{3}}{3} \operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{x + 1}\right|} - \frac{\sqrt{2}}{\left|{x + 1}\right|} \right)} 
(sqrt(3)/3)*asinh(-sqrt(2)/|x + 1| + x*sqrt(2)/(2*|x + 1|))
Denominador común [src] 
           /     ___         ___ \
  ___      |   \/ 2      x*\/ 2  |
\/ 3 *asinh|- ------- + ---------|
           \  |1 + x|   2*|1 + x|/
----------------------------------
                3
3asinh⁡(2x2∣x+1∣−2∣x+1∣)3\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{x + 1}\right|} - \frac{\sqrt{2}}{\left|{x + 1}\right|} \right)}}{3} 
sqrt(3)*asinh(-sqrt(2)/|1 + x| + x*sqrt(2)/(2*|1 + x|))/3
Denominador racional [src] 
           /  ___         \
  ___      |\/ 2 *(-2 + x)|
\/ 3 *asinh|--------------|
           \  2*|1 + x|   /
---------------------------
             3
3asinh⁡(2(x−2)2∣x+1∣)3\frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{2} \left(x - 2\right)}{2 \left|{x + 1}\right|} \right)}}{3} 
sqrt(3)*asinh(sqrt(2)*(-2 + x)/(2*|1 + x|))/3
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