Sr Examen

Otras calculadoras

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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
     /    x           2    \                  
asinh|--------- + ---------|      ____________
     |  ___         ___    |     /  2         
     \\/ 3 *|x|   \/ 3 *|x|/   \/  x  + x + 1 
---------------------------- - ---------------
             2                        x
asinh⁡(x3∣x∣+23∣x∣)2−(x2+x)+1x\frac{\operatorname{asinh}{\left(\frac{x}{\sqrt{3} \left|{x}\right|} + \frac{2}{\sqrt{3} \left|{x}\right|} \right)}}{2} - \frac{\sqrt{\left(x^{2} + x\right) + 1}}{x} 
asinh(x/((sqrt(3)*|x|)) + 2/((sqrt(3)*|x|)))/2 - sqrt(x^2 + x + 1)/x
Simplificación general [src] 
                           /  ___        \
                           |\/ 3 *(2 + x)|
     ____________   x*asinh|-------------|
    /          2           \    3*|x|    /
- \/  1 + x + x   + ----------------------
                              2           
------------------------------------------
                    x
xasinh⁡(3(x+2)3∣x∣)2−x2+x+1x\frac{\frac{x \operatorname{asinh}{\left(\frac{\sqrt{3} \left(x + 2\right)}{3 \left|{x}\right|} \right)}}{2} - \sqrt{x^{2} + x + 1}}{x} 
(-sqrt(1 + x + x^2) + x*asinh(sqrt(3)*(2 + x)/(3*|x|))/2)/x
Parte trigonométrica [src] 
     /    ___       ___\                  
     |2*\/ 3    x*\/ 3 |      ____________
asinh|------- + -------|     /          2 
     \ 3*|x|     3*|x| /   \/  1 + x + x  
------------------------ - ---------------
           2                      x
asinh⁡(3x3∣x∣+233∣x∣)2−x2+x+1x\frac{\operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}}{2} - \frac{\sqrt{x^{2} + x + 1}}{x} 
asinh(2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))/2 - sqrt(1 + x + x^2)/x
Abrimos la expresión [src] 
     /    ___       ___\                  
     |2*\/ 3    x*\/ 3 |      ____________
asinh|------- + -------|     /  2         
     \ 3*|x|     3*|x| /   \/  x  + x + 1 
------------------------ - ---------------
           2                      x
asinh⁡(3x3∣x∣+233∣x∣)2−(x2+x)+1x\frac{\operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}}{2} - \frac{\sqrt{\left(x^{2} + x\right) + 1}}{x} 
asinh(2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))/2 - sqrt(x^2 + x + 1)/x
Denominador común [src] 
     /    ___       ___\                  
     |2*\/ 3    x*\/ 3 |      ____________
asinh|------- + -------|     /          2 
     \ 3*|x|     3*|x| /   \/  1 + x + x  
------------------------ - ---------------
           2                      x
asinh⁡(3x3∣x∣+233∣x∣)2−x2+x+1x\frac{\operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}}{2} - \frac{\sqrt{x^{2} + x + 1}}{x} 
asinh(2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))/2 - sqrt(1 + x + x^2)/x
Potencias [src] 
     /    ___       ___\                  
     |2*\/ 3    x*\/ 3 |      ____________
asinh|------- + -------|     /          2 
     \ 3*|x|     3*|x| /   \/  1 + x + x  
------------------------ - ---------------
           2                      x
asinh⁡(3x3∣x∣+233∣x∣)2−x2+x+1x\frac{\operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}}{2} - \frac{\sqrt{x^{2} + x + 1}}{x} 
asinh(2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))/2 - sqrt(1 + x + x^2)/x
Compilar la expresión [src] 
     /    x           2    \                  
asinh|--------- + ---------|      ____________
     |  ___         ___    |     /          2 
     \\/ 3 *|x|   \/ 3 *|x|/   \/  1 + x + x  
---------------------------- - ---------------
             2                        x
asinh⁡(x3∣x∣+23∣x∣)2−x2+x+1x\frac{\operatorname{asinh}{\left(\frac{x}{\sqrt{3} \left|{x}\right|} + \frac{2}{\sqrt{3} \left|{x}\right|} \right)}}{2} - \frac{\sqrt{x^{2} + x + 1}}{x} 
asinh(x/((sqrt(3)*|x|)) + 2/((sqrt(3)*|x|)))/2 - sqrt(1 + x + x^2)/x
Respuesta numérica [src] 
0.5*asinh(x/((sqrt(3)*|x|)) + 2/((sqrt(3)*|x|))) - (1.0 + x + x^2)^0.5/x
0.5*asinh(x/((sqrt(3)*|x|)) + 2/((sqrt(3)*|x|))) - (1.0 + x + x^2)^0.5/x
Unión de expresiones racionales [src] 
                               /  ___        \
      _______________          |\/ 3 *(2 + x)|
- 2*\/ 1 + x*(1 + x)  + x*asinh|-------------|
                               \    3*|x|    /
----------------------------------------------
                     2*x
xasinh⁡(3(x+2)3∣x∣)−2x(x+1)+12x\frac{x \operatorname{asinh}{\left(\frac{\sqrt{3} \left(x + 2\right)}{3 \left|{x}\right|} \right)} - 2 \sqrt{x \left(x + 1\right) + 1}}{2 x} 
(-2*sqrt(1 + x*(1 + x)) + x*asinh(sqrt(3)*(2 + x)/(3*|x|)))/(2*x)
Denominador racional [src] 
       ____________          /    ___       ___\
      /          2           |2*\/ 3    x*\/ 3 |
- 2*\/  1 + x + x   + x*asinh|------- + -------|
                             \ 3*|x|     3*|x| /
------------------------------------------------
                      2*x
xasinh⁡(3x3∣x∣+233∣x∣)−2x2+x+12x\frac{x \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)} - 2 \sqrt{x^{2} + x + 1}}{2 x} 
(-2*sqrt(1 + x + x^2) + x*asinh(2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|)))/(2*x)
Combinatoria [src] 
       ____________          /    ___       ___\
      /          2           |2*\/ 3    x*\/ 3 |
- 2*\/  1 + x + x   + x*asinh|------- + -------|
                             \ 3*|x|     3*|x| /
------------------------------------------------
                      2*x
xasinh⁡(3x3∣x∣+233∣x∣)−2x2+x+12x\frac{x \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)} - 2 \sqrt{x^{2} + x + 1}}{2 x} 
(-2*sqrt(1 + x + x^2) + x*asinh(2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|)))/(2*x)
    © Sr Examen – Калькулятор