Sr Examen
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?
Solución
Ha introducido
[src]
/ x 2 \
asinh|--------- + ---------| ____________
| ___ ___ | / 2
\\/ 3 *|x| \/ 3 *|x|/ \/ x + x + 1
---------------------------- - ---------------
2 x
$$\frac{\operatorname{asinh}{\left(\frac{x}{\sqrt{3} \left|{x}\right|} + \frac{2}{\sqrt{3} \left|{x}\right|} \right)}}{2} - \frac{\sqrt{\left(x^{2} + x\right) + 1}}{x}$$
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
$$\frac{\frac{x \operatorname{asinh}{\left(\frac{\sqrt{3} \left(x + 2\right)}{3 \left|{x}\right|} \right)}}{2} - \sqrt{x^{2} + x + 1}}{x}$$
(-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
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}}{2} - \frac{\sqrt{x^{2} + x + 1}}{x}$$
asinh(2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|))/2 - sqrt(1 + x + x^2)/x
Denominador común
[src]
/ ___ ___\
|2*\/ 3 x*\/ 3 | ____________
asinh|------- + -------| / 2
\ 3*|x| 3*|x| / \/ 1 + x + x
------------------------ - ---------------
2 x
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}}{2} - \frac{\sqrt{x^{2} + x + 1}}{x}$$
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
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)}}{2} - \frac{\sqrt{x^{2} + x + 1}}{x}$$
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
$$\frac{\operatorname{asinh}{\left(\frac{x}{\sqrt{3} \left|{x}\right|} + \frac{2}{\sqrt{3} \left|{x}\right|} \right)}}{2} - \frac{\sqrt{x^{2} + x + 1}}{x}$$
asinh(x/((sqrt(3)*|x|)) + 2/((sqrt(3)*|x|)))/2 - sqrt(1 + x + x^2)/x
Respuesta numérica
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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
$$\frac{x \operatorname{asinh}{\left(\frac{\sqrt{3} \left(x + 2\right)}{3 \left|{x}\right|} \right)} - 2 \sqrt{x \left(x + 1\right) + 1}}{2 x}$$
(-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
$$\frac{x \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)} - 2 \sqrt{x^{2} + x + 1}}{2 x}$$
(-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
$$\frac{x \operatorname{asinh}{\left(\frac{\sqrt{3} x}{3 \left|{x}\right|} + \frac{2 \sqrt{3}}{3 \left|{x}\right|} \right)} - 2 \sqrt{x^{2} + x + 1}}{2 x}$$
(-2*sqrt(1 + x + x^2) + x*asinh(2*sqrt(3)/(3*|x|) + x*sqrt(3)/(3*|x|)))/(2*x)