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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                                    /2*x - 1\                  
                               asinh|-------|                  
                                    |   ___ |      ____________
     /    x           2    \        \ \/ 3  /     /  2         
asinh|--------- - ---------| - -------------- + \/  x  - x + 1 
     |  ___         ___    |         2                         
     \\/ 3 *|x|   \/ 3 *|x|/
$$\left(- \frac{\operatorname{asinh}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}}{2} + \operatorname{asinh}{\left(\frac{x}{\sqrt{3} \left|{x}\right|} - \frac{2}{\sqrt{3} \left|{x}\right|} \right)}\right) + \sqrt{\left(x^{2} - x\right) + 1}$$ 
asinh(x/((sqrt(3)*|x|)) - 2*sqrt(3)/(3*|x|)) - asinh((2*x - 1)/sqrt(3))/2 + sqrt(x^2 - x + 1)
Simplificación general [src] 
                       /  ___           \                        
                       |\/ 3 *(-1 + 2*x)|                        
   ____________   asinh|----------------|        /  ___         \
  /      2             \       3        /        |\/ 3 *(-2 + x)|
\/  1 + x  - x  - ----------------------- + asinh|--------------|
                             2                   \    3*|x|     /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} \left(x - 2\right)}{3 \left|{x}\right|} \right)}$$ 
sqrt(1 + x^2 - x) - asinh(sqrt(3)*(-1 + 2*x)/3)/2 + asinh(sqrt(3)*(-2 + x)/(3*|x|))
Respuesta numérica [src] 
(1.0 + x^2 - x)^0.5 - 0.5*asinh((2*x - 1)/sqrt(3)) + asinh(x/((sqrt(3)*|x|)) - 2*sqrt(3)/(3*|x|))
(1.0 + x^2 - x)^0.5 - 0.5*asinh((2*x - 1)/sqrt(3)) + asinh(x/((sqrt(3)*|x|)) - 2*sqrt(3)/(3*|x|))
Denominador racional [src] 
       /    ___         ___\        ____________          /      ___       ___\
       |  \/ 3    2*x*\/ 3 |       /      2               |  2*\/ 3    x*\/ 3 |
- asinh|- ----- + ---------| + 2*\/  1 + x  - x  + 2*asinh|- ------- + -------|
       \    3         3    /                              \   3*|x|     3*|x| /
-------------------------------------------------------------------------------
                                       2
$$\frac{2 \sqrt{x^{2} - x + 1} - \operatorname{asinh}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 2 \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}}{2}$$ 
(-asinh(-sqrt(3)/3 + 2*x*sqrt(3)/3) + 2*sqrt(1 + x^2 - x) + 2*asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|)))/2
Abrimos la expresión [src] 
                       /2*x - 1\                             
                  asinh|-------|                             
   ____________        |   ___ |        /      ___       ___\
  /  2                 \ \/ 3  /        |  2*\/ 3    x*\/ 3 |
\/  x  - x + 1  - -------------- + asinh|- ------- + -------|
                        2               \   3*|x|     3*|x| /
$$\sqrt{\left(x^{2} - x\right) + 1} - \frac{\operatorname{asinh}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$ 
sqrt(x^2 - x + 1) - asinh((2*x - 1)/sqrt(3))/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))
Compilar la expresión [src] 
                       /2*x - 1\                               
                  asinh|-------|                               
   ____________        |   ___ |                               
  /      2             \ \/ 3  /        /    x           2    \
\/  1 + x  - x  - -------------- + asinh|--------- - ---------|
                        2               |  ___         ___    |
                                        \\/ 3 *|x|   \/ 3 *|x|/
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}}{2} + \operatorname{asinh}{\left(\frac{x}{\sqrt{3} \left|{x}\right|} - \frac{2}{\sqrt{3} \left|{x}\right|} \right)}$$ 
sqrt(1 + x^2 - x) - asinh((2*x - 1)/sqrt(3))/2 + asinh(x/((sqrt(3)*|x|)) - 2*sqrt(3)/(3*|x|))
Parte trigonométrica [src] 
                       /  ___           \                             
                       |\/ 3 *(-1 + 2*x)|                             
   ____________   asinh|----------------|        /      ___       ___\
  /      2             \       3        /        |  2*\/ 3    x*\/ 3 |
\/  1 + x  - x  - ----------------------- + asinh|- ------- + -------|
                             2                   \   3*|x|     3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$ 
sqrt(1 + x^2 - x) - asinh(sqrt(3)*(-1 + 2*x)/3)/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))
Unión de expresiones racionales [src] 
       /  ___           \                                 /  ___         \
       |\/ 3 *(-1 + 2*x)|       ________________          |\/ 3 *(-2 + x)|
- asinh|----------------| + 2*\/ 1 + x*(-1 + x)  + 2*asinh|--------------|
       \       3        /                                 \    3*|x|     /
--------------------------------------------------------------------------
                                    2
$$\frac{2 \sqrt{x \left(x - 1\right) + 1} - \operatorname{asinh}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)} + 2 \operatorname{asinh}{\left(\frac{\sqrt{3} \left(x - 2\right)}{3 \left|{x}\right|} \right)}}{2}$$ 
(-asinh(sqrt(3)*(-1 + 2*x)/3) + 2*sqrt(1 + x*(-1 + x)) + 2*asinh(sqrt(3)*(-2 + x)/(3*|x|)))/2
Potencias [src] 
                       /  ___ /  1   2*x\\                             
   ____________   asinh|\/ 3 *|- - + ---||        /      ___       ___\
  /      2             \      \  3    3 //        |  2*\/ 3    x*\/ 3 |
\/  1 + x  - x  - ------------------------ + asinh|- ------- + -------|
                             2                    \   3*|x|     3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\sqrt{3} \left(\frac{2 x}{3} - \frac{1}{3}\right) \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$ 
                       /  ___           \                             
                       |\/ 3 *(-1 + 2*x)|                             
   ____________   asinh|----------------|        /      ___       ___\
  /      2             \       3        /        |  2*\/ 3    x*\/ 3 |
\/  1 + x  - x  - ----------------------- + asinh|- ------- + -------|
                             2                   \   3*|x|     3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$ 
sqrt(1 + x^2 - x) - asinh(sqrt(3)*(-1 + 2*x)/3)/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))
Combinatoria [src] 
                       /    ___         ___\                             
                       |  \/ 3    2*x*\/ 3 |                             
   ____________   asinh|- ----- + ---------|        /      ___       ___\
  /      2             \    3         3    /        |  2*\/ 3    x*\/ 3 |
\/  1 + x  - x  - -------------------------- + asinh|- ------- + -------|
                              2                     \   3*|x|     3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$ 
sqrt(1 + x^2 - x) - asinh(-sqrt(3)/3 + 2*x*sqrt(3)/3)/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))
Denominador común [src] 
                       /    ___         ___\                             
                       |  \/ 3    2*x*\/ 3 |                             
   ____________   asinh|- ----- + ---------|        /      ___       ___\
  /      2             \    3         3    /        |  2*\/ 3    x*\/ 3 |
\/  1 + x  - x  - -------------------------- + asinh|- ------- + -------|
                              2                     \   3*|x|     3*|x| /
$$\sqrt{x^{2} - x + 1} - \frac{\operatorname{asinh}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{2} + \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} - \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}$$ 
sqrt(1 + x^2 - x) - asinh(-sqrt(3)/3 + 2*x*sqrt(3)/3)/2 + asinh(-2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))
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