Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(2)/(4*x^(3/2)*sqrt(1-1/(2*x))*acos(1/(sqrt(2*x))))
¿Cómo vas a descomponer esta sqrt(2)/(4*x^(3/2)*sqrt(1-1/(2*x))*acos(1/(sqrt(2*x)))) expresión en fracciones?
Solución
Ha introducido
[src]
___
\/ 2
----------------------------------
_________
3/2 / 1 / 1 \
4*x * / 1 - --- *acos|-------|
\/ 2*x | _____|
\\/ 2*x /
$$\frac{\sqrt{2}}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{1}{\sqrt{2 x}} \right)}}$$
sqrt(2)/((((4*x^(3/2))*sqrt(1 - 1/(2*x)))*acos(1/(sqrt(2*x)))))
Simplificación general
[src]
1
--------------------------------
_______ / ___ \
3/2 / 1 | \/ 2 |
2*x * / 2 - - *acos|-------|
\/ x | ___|
\2*\/ x /
$$\frac{1}{2 x^{\frac{3}{2}} \sqrt{2 - \frac{1}{x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
1/(2*x^(3/2)*sqrt(2 - 1/x)*acos(sqrt(2)/(2*sqrt(x))))
Respuesta numérica
[src]
0.353553390593274*x^(-1.5)*(1.0 - 0.5/x)^(-0.5)/acos(1/(sqrt(2*x)))
0.353553390593274*x^(-1.5)*(1.0 - 0.5/x)^(-0.5)/acos(1/(sqrt(2*x)))
Combinatoria
[src]
1
--------------------------------
_______ / ___ \
3/2 / 1 | \/ 2 |
2*x * / 2 - - *acos|-------|
\/ x | ___|
\2*\/ x /
$$\frac{1}{2 x^{\frac{3}{2}} \sqrt{2 - \frac{1}{x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
1/(2*x^(3/2)*sqrt(2 - 1/x)*acos(sqrt(2)/(2*sqrt(x))))
Denominador racional
[src]
____
___ / 3
\/ 2 *\/ x
------------------------------------
_________ / ___ ___\
3 / 1 |\/ 2 *\/ x |
4*x * / 1 - --- *acos|-----------|
\/ 2*x \ 2*x /
$$\frac{\sqrt{2} \sqrt{x^{3}}}{4 x^{3} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{\sqrt{2} \sqrt{x}}{2 x} \right)}}$$
sqrt(2)*sqrt(x^3)/(4*x^3*sqrt(1 - 1/(2*x))*acos(sqrt(2)*sqrt(x)/(2*x)))
Denominador común
[src]
___
\/ 2
----------------------------------
_________ / ___ \
3/2 / 1 | \/ 2 |
4*x * / 1 - --- *acos|-------|
\/ 2*x | ___|
\2*\/ x /
$$\frac{\sqrt{2}}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
sqrt(2)/(4*x^(3/2)*sqrt(1 - 1/(2*x))*acos(sqrt(2)/(2*sqrt(x))))
Potencias
[src]
___
\/ 2
----------------------------------
_________ / ___ \
3/2 / 1 | \/ 2 |
4*x * / 1 - --- *acos|-------|
\/ 2*x | ___|
\2*\/ x /
$$\frac{\sqrt{2}}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
sqrt(2)/(4*x^(3/2)*sqrt(1 - 1/(2*x))*acos(sqrt(2)/(2*sqrt(x))))
Unión de expresiones racionales
[src]
1
-----------------------------------
__________ / ___ \
3/2 / -1 + 2*x | \/ 2 |
2*x * / -------- *acos|-------|
\/ x | ___|
\2*\/ x /
$$\frac{1}{2 x^{\frac{3}{2}} \sqrt{\frac{2 x - 1}{x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
1/(2*x^(3/2)*sqrt((-1 + 2*x)/x)*acos(sqrt(2)/(2*sqrt(x))))
Parte trigonométrica
[src]
___
\/ 2
----------------------------------
_________ / ___ \
3/2 / 1 | \/ 2 |
4*x * / 1 - --- *acos|-------|
\/ 2*x | ___|
\2*\/ x /
$$\frac{\sqrt{2}}{4 x^{\frac{3}{2}} \sqrt{1 - \frac{1}{2 x}} \operatorname{acos}{\left(\frac{\sqrt{2}}{2 \sqrt{x}} \right)}}$$
sqrt(2)/(4*x^(3/2)*sqrt(1 - 1/(2*x))*acos(sqrt(2)/(2*sqrt(x))))