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Simplificación de expresiones/ Descomposición en fracciones simples/ asinh(x/(2*|x+1|)-2/|x+1|)/sqrt(5)

¿Cómo vas a descomponer esta asinh(x/(2*|x+1|)-2/|x+1|)/sqrt(5) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     /    x          2   \
asinh|--------- - -------|
     \2*|x + 1|   |x + 1|/
--------------------------
            ___           
          \/ 5
$$\frac{\operatorname{asinh}{\left(\frac{x}{2 \left|{x + 1}\right|} - \frac{2}{\left|{x + 1}\right|} \right)}}{\sqrt{5}}$$ 
asinh(x/((2*|x + 1|)) - 2/|x + 1|)/sqrt(5)
Simplificación general [src] 
  ___      /  -4 + x \
\/ 5 *asinh|---------|
           \2*|1 + x|/
----------------------
          5
$$\frac{\sqrt{5} \operatorname{asinh}{\left(\frac{x - 4}{2 \left|{x + 1}\right|} \right)}}{5}$$ 
sqrt(5)*asinh((-4 + x)/(2*|1 + x|))/5
Descomposición de una fracción [src] 
sqrt(5)*asinh(-2/|x + 1| + x/(2*|x + 1|))/5
$$\frac{\sqrt{5} \operatorname{asinh}{\left(\frac{x}{2 \left|{x + 1}\right|} - \frac{2}{\left|{x + 1}\right|} \right)}}{5}$$ 
  ___      /     2          x    \
\/ 5 *asinh|- ------- + ---------|
           \  |x + 1|   2*|x + 1|/
----------------------------------
                5
Respuesta numérica [src] 
0.447213595499958*asinh(x/((2*|x + 1|)) - 2/|x + 1|)
0.447213595499958*asinh(x/((2*|x + 1|)) - 2/|x + 1|)
Denominador común [src] 
  ___      /     2          x    \
\/ 5 *asinh|- ------- + ---------|
           \  |1 + x|   2*|1 + x|/
----------------------------------
                5
$$\frac{\sqrt{5} \operatorname{asinh}{\left(\frac{x}{2 \left|{x + 1}\right|} - \frac{2}{\left|{x + 1}\right|} \right)}}{5}$$ 
sqrt(5)*asinh(-2/|1 + x| + x/(2*|1 + x|))/5
Abrimos la expresión [src] 
  ___                             
\/ 5       /     2          x    \
-----*asinh|- ------- + ---------|
  5        \  |x + 1|   2*|x + 1|/
$$\frac{\sqrt{5}}{5} \operatorname{asinh}{\left(\frac{x}{2 \left|{x + 1}\right|} - \frac{2}{\left|{x + 1}\right|} \right)}$$ 
(sqrt(5)/5)*asinh(-2/|x + 1| + x/(2*|x + 1|))
Denominador racional [src] 
  ___      /  -4 + x \
\/ 5 *asinh|---------|
           \2*|1 + x|/
----------------------
          5
$$\frac{\sqrt{5} \operatorname{asinh}{\left(\frac{x - 4}{2 \left|{x + 1}\right|} \right)}}{5}$$ 
sqrt(5)*asinh((-4 + x)/(2*|1 + x|))/5
Parte trigonométrica [src] 
  ___      /     2          x    \
\/ 5 *asinh|- ------- + ---------|
           \  |1 + x|   2*|1 + x|/
----------------------------------
                5
$$\frac{\sqrt{5} \operatorname{asinh}{\left(\frac{x}{2 \left|{x + 1}\right|} - \frac{2}{\left|{x + 1}\right|} \right)}}{5}$$ 
sqrt(5)*asinh(-2/|1 + x| + x/(2*|1 + x|))/5
Unión de expresiones racionales [src] 
  ___      /  -4 + x \
\/ 5 *asinh|---------|
           \2*|1 + x|/
----------------------
          5
$$\frac{\sqrt{5} \operatorname{asinh}{\left(\frac{x - 4}{2 \left|{x + 1}\right|} \right)}}{5}$$ 
sqrt(5)*asinh((-4 + x)/(2*|1 + x|))/5
Combinatoria [src] 
  ___      /     2          x    \
\/ 5 *asinh|- ------- + ---------|
           \  |1 + x|   2*|1 + x|/
----------------------------------
                5
$$\frac{\sqrt{5} \operatorname{asinh}{\left(\frac{x}{2 \left|{x + 1}\right|} - \frac{2}{\left|{x + 1}\right|} \right)}}{5}$$ 
sqrt(5)*asinh(-2/|1 + x| + x/(2*|1 + x|))/5
Compilar la expresión [src] 
  ___      /    x          2   \
\/ 5 *asinh|--------- - -------|
           \2*|x + 1|   |x + 1|/
--------------------------------
               5
$$\frac{\sqrt{5} \operatorname{asinh}{\left(\frac{x}{2 \left|{x + 1}\right|} - \frac{2}{\left|{x + 1}\right|} \right)}}{5}$$ 
sqrt(5)*asinh(x/((2*|x + 1|)) - 2/|x + 1|)/5
Potencias [src] 
  ___      /     2          x    \
\/ 5 *asinh|- ------- + ---------|
           \  |1 + x|   2*|1 + x|/
----------------------------------
                5
$$\frac{\sqrt{5} \operatorname{asinh}{\left(\frac{x}{2 \left|{x + 1}\right|} - \frac{2}{\left|{x + 1}\right|} \right)}}{5}$$ 
sqrt(5)*asinh(-2/|1 + x| + x/(2*|1 + x|))/5
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