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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(3*x^2-6*x+4)/3-asinh((6*x-6)/(2*sqrt(3)))/sqrt(3)

¿Cómo vas a descomponer esta sqrt(3*x^2-6*x+4)/3-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*x  - 6*x + 4         \2*\/ 3 /
------------------- - --------------
         3                  ___     
                          \/ 3
$$\frac{\sqrt{\left(3 x^{2} - 6 x\right) + 4}}{3} - \frac{\operatorname{asinh}{\left(\frac{6 x - 6}{2 \sqrt{3}} \right)}}{\sqrt{3}}$$ 
sqrt(3*x^2 - 6*x + 4)/3 - asinh((6*x - 6)/((2*sqrt(3))))/sqrt(3)
Simplificación general [src] 
   ________________                              
  /              2      ___      /  ___         \
\/  4 - 6*x + 3*x     \/ 3 *asinh\\/ 3 *(-1 + x)/
------------------- - ---------------------------
         3                         3
$$\frac{\sqrt{3 x^{2} - 6 x + 4}}{3} - \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} \left(x - 1\right) \right)}}{3}$$ 
sqrt(4 - 6*x + 3*x^2)/3 - sqrt(3)*asinh(sqrt(3)*(-1 + x))/3
Denominador común [src] 
   ________________                                 
  /              2      ___      /    ___       ___\
\/  4 - 6*x + 3*x     \/ 3 *asinh\- \/ 3  + x*\/ 3 /
------------------- - ------------------------------
         3                          3
$$\frac{\sqrt{3 x^{2} - 6 x + 4}}{3} - \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x - \sqrt{3} \right)}}{3}$$ 
sqrt(4 - 6*x + 3*x^2)/3 - sqrt(3)*asinh(-sqrt(3) + x*sqrt(3))/3
Compilar la expresión [src] 
                        ___      /6*x - 6\
   ________________   \/ 3 *asinh|-------|
  /              2               |    ___|
\/  4 - 6*x + 3*x                \2*\/ 3 /
------------------- - --------------------
         3                     3
$$\frac{\sqrt{3 x^{2} - 6 x + 4}}{3} - \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{6 x - 6}{2 \sqrt{3}} \right)}}{3}$$ 
sqrt(4 - 6*x + 3*x^2)/3 - sqrt(3)*asinh((6*x - 6)/((2*sqrt(3))))/3
Abrimos la expresión [src] 
   ________________                               
  /    2                ___      /  ___          \
\/  3*x  - 6*x + 4    \/ 3       |\/ 3 *(6*x - 6)|
------------------- - -----*asinh|---------------|
         3              3        \       6       /
$$\frac{\sqrt{\left(3 x^{2} - 6 x\right) + 4}}{3} - \frac{\sqrt{3}}{3} \operatorname{asinh}{\left(\frac{\sqrt{3} \left(6 x - 6\right)}{6} \right)}$$ 
sqrt(3*x^2 - 6*x + 4)/3 - sqrt(3)/3*asinh(sqrt(3)*(6*x - 6)/6)
Unión de expresiones racionales [src] 
  __________________     ___      /  ___         \
\/ 4 + 3*x*(-2 + x)  - \/ 3 *asinh\\/ 3 *(-1 + x)/
--------------------------------------------------
                        3
$$\frac{\sqrt{3 x \left(x - 2\right) + 4} - \sqrt{3} \operatorname{asinh}{\left(\sqrt{3} \left(x - 1\right) \right)}}{3}$$ 
(sqrt(4 + 3*x*(-2 + x)) - sqrt(3)*asinh(sqrt(3)*(-1 + x)))/3
Combinatoria [src] 
   ________________                                 
  /              2      ___      /    ___       ___\
\/  4 - 6*x + 3*x     \/ 3 *asinh\- \/ 3  + x*\/ 3 /
------------------- - ------------------------------
         3                          3
$$\frac{\sqrt{3 x^{2} - 6 x + 4}}{3} - \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x - \sqrt{3} \right)}}{3}$$ 
sqrt(4 - 6*x + 3*x^2)/3 - sqrt(3)*asinh(-sqrt(3) + x*sqrt(3))/3
Parte trigonométrica [src] 
                                 /  ___           \
   ________________     ___      |\/ 3 *(-6 + 6*x)|
  /              2    \/ 3 *asinh|----------------|
\/  4 - 6*x + 3*x                \       6        /
------------------- - -----------------------------
         3                          3
$$\frac{\sqrt{3 x^{2} - 6 x + 4}}{3} - \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{3} \left(6 x - 6\right)}{6} \right)}}{3}$$ 
sqrt(4 - 6*x + 3*x^2)/3 - sqrt(3)*asinh(sqrt(3)*(-6 + 6*x)/6)/3
Respuesta numérica [src] 
0.816496580927726*(0.666666666666667 - x + 0.5*x^2)^0.5 - 0.577350269189626*asinh((6*x - 6)/((2*sqrt(3))))
0.816496580927726*(0.666666666666667 - x + 0.5*x^2)^0.5 - 0.577350269189626*asinh((6*x - 6)/((2*sqrt(3))))
Denominador racional [src] 
   ________________                                 
  /              2      ___      /    ___       ___\
\/  4 - 6*x + 3*x   - \/ 3 *asinh\- \/ 3  + x*\/ 3 /
----------------------------------------------------
                         3
$$\frac{\sqrt{3 x^{2} - 6 x + 4} - \sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x - \sqrt{3} \right)}}{3}$$ 
(sqrt(4 - 6*x + 3*x^2) - sqrt(3)*asinh(-sqrt(3) + x*sqrt(3)))/3
Potencias [src] 
   ________________                              
  /              2      ___      /  ___         \
\/  4 - 6*x + 3*x     \/ 3 *asinh\\/ 3 *(-1 + x)/
------------------- - ---------------------------
         3                         3
$$\frac{\sqrt{3 x^{2} - 6 x + 4}}{3} - \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} \left(x - 1\right) \right)}}{3}$$ 
                                 /  ___           \
   ________________     ___      |\/ 3 *(-6 + 6*x)|
  /              2    \/ 3 *asinh|----------------|
\/  4 - 6*x + 3*x                \       6        /
------------------- - -----------------------------
         3                          3
$$\frac{\sqrt{3 x^{2} - 6 x + 4}}{3} - \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{3} \left(6 x - 6\right)}{6} \right)}}{3}$$ 
sqrt(4 - 6*x + 3*x^2)/3 - sqrt(3)*asinh(sqrt(3)*(-6 + 6*x)/6)/3
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