Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(x/(1+x))*(1+x)*(1/(2*(1+x))-x/(2*(1+x)^2))/(x*sqrt(1-x/(1+x)))
¿Cómo vas a descomponer esta sqrt(x/(1+x))*(1+x)*(1/(2*(1+x))-x/(2*(1+x)^2))/(x*sqrt(1-x/(1+x))) expresión en fracciones?
Solución
Ha introducido
[src]
_______
/ x / 1 x \
/ ----- *(1 + x)*|--------- - ----------|
\/ 1 + x |2*(1 + x) 2|
\ 2*(1 + x) /
--------------------------------------------
___________
/ x
x* / 1 - -----
\/ 1 + x
$$\frac{\sqrt{\frac{x}{x + 1}} \left(x + 1\right) \left(- \frac{x}{2 \left(x + 1\right)^{2}} + \frac{1}{2 \left(x + 1\right)}\right)}{x \sqrt{- \frac{x}{x + 1} + 1}}$$
((sqrt(x/(1 + x))*(1 + x))*(1/(2*(1 + x)) - x/(2*(1 + x)^2)))/((x*sqrt(1 - x/(1 + x))))
Simplificación general
[src]
_______
/ x
/ -----
\/ 1 + x
-----------------------
_______
/ 1
2*x* / ----- *(1 + x)
\/ 1 + x
$$\frac{\sqrt{\frac{x}{x + 1}}}{2 x \left(x + 1\right) \sqrt{\frac{1}{x + 1}}}$$
sqrt(x/(1 + x))/(2*x*sqrt(1/(1 + x))*(1 + x))
Respuesta numérica
[src]
(x/(1.0 + x))^0.5*(1.0 - x/(1.0 + x))^(-0.5)*(1.0 + x)*(1/(2.0 + 2.0*x) - 0.5*x/(1.0 + x)^2)/x
(x/(1.0 + x))^0.5*(1.0 - x/(1.0 + x))^(-0.5)*(1.0 + x)*(1/(2.0 + 2.0*x) - 0.5*x/(1.0 + x)^2)/x
Compilar la expresión
[src]
_______
/ x / 1 x \
/ ----- *(1 + x)*|------- - ----------|
\/ 1 + x |2 + 2*x 2|
\ 2*(1 + x) /
------------------------------------------
___________
/ x
x* / 1 - -----
\/ 1 + x
$$\frac{\sqrt{\frac{x}{x + 1}} \left(x + 1\right) \left(- \frac{x}{2 \left(x + 1\right)^{2}} + \frac{1}{2 x + 2}\right)}{x \sqrt{- \frac{x}{x + 1} + 1}}$$
sqrt(x/(1 + x))*(1 + x)*(1/(2 + 2*x) - x/(2*(1 + x)^2))/(x*sqrt(1 - x/(1 + x)))
Parte trigonométrica
[src]
_______
/ x / 1 x \
/ ----- *(1 + x)*|------- - ----------|
\/ 1 + x |2 + 2*x 2|
\ 2*(1 + x) /
------------------------------------------
___________
/ x
x* / 1 - -----
\/ 1 + x
$$\frac{\sqrt{\frac{x}{x + 1}} \left(x + 1\right) \left(- \frac{x}{2 \left(x + 1\right)^{2}} + \frac{1}{2 x + 2}\right)}{x \sqrt{- \frac{x}{x + 1} + 1}}$$
sqrt(x/(1 + x))*(1 + x)*(1/(2 + 2*x) - x/(2*(1 + x)^2))/(x*sqrt(1 - x/(1 + x)))
Denominador racional
[src]
_______ ___________ _______ ___________ _______ ___________
/ x 2 / x / x / x 2 / x / x
- 2* / ----- *(1 + x) * / 1 - ----- + 2*x* / ----- * / 1 - ----- + 2*x * / ----- * / 1 - -----
\/ 1 + x \/ 1 + x \/ 1 + x \/ 1 + x \/ 1 + x \/ 1 + x
-------------------------------------------------------------------------------------------------------------
/ x \
2*x*(1 + x)*|-1 + -----|*(2 + 2*x)
\ 1 + x/
$$\frac{2 x^{2} \sqrt{\frac{x}{x + 1}} \sqrt{- \frac{x}{x + 1} + 1} + 2 x \sqrt{\frac{x}{x + 1}} \sqrt{- \frac{x}{x + 1} + 1} - 2 \sqrt{\frac{x}{x + 1}} \left(x + 1\right)^{2} \sqrt{- \frac{x}{x + 1} + 1}}{2 x \left(x + 1\right) \left(2 x + 2\right) \left(\frac{x}{x + 1} - 1\right)}$$
(-2*sqrt(x/(1 + x))*(1 + x)^2*sqrt(1 - x/(1 + x)) + 2*x*sqrt(x/(1 + x))*sqrt(1 - x/(1 + x)) + 2*x^2*sqrt(x/(1 + x))*sqrt(1 - x/(1 + x)))/(2*x*(1 + x)*(-1 + x/(1 + x))*(2 + 2*x))
Combinatoria
[src]
_______
/ x
/ -----
\/ 1 + x
-----------------------
_______
/ 1
2*x* / ----- *(1 + x)
\/ 1 + x
$$\frac{\sqrt{\frac{x}{x + 1}}}{2 x \left(x + 1\right) \sqrt{\frac{1}{x + 1}}}$$
sqrt(x/(1 + x))/(2*x*sqrt(1/(1 + x))*(1 + x))
Denominador común
[src]
_______ ___________
/ x / x
/ ----- * / 1 - -----
\/ 1 + x \/ 1 + x
---------------------------
2*x
$$\frac{\sqrt{\frac{x}{x + 1}} \sqrt{- \frac{x}{x + 1} + 1}}{2 x}$$
sqrt(x/(1 + x))*sqrt(1 - x/(1 + x))/(2*x)
Unión de expresiones racionales
[src]
_______
/ x
/ -----
\/ 1 + x
-----------------------
_______
/ 1
2*x* / ----- *(1 + x)
\/ 1 + x
$$\frac{\sqrt{\frac{x}{x + 1}}}{2 x \left(x + 1\right) \sqrt{\frac{1}{x + 1}}}$$
sqrt(x/(1 + x))/(2*x*sqrt(1/(1 + x))*(1 + x))
Potencias
[src]
_______
/ x / 1 x \
/ ----- *(1 + x)*|------- - ----------|
\/ 1 + x |2 + 2*x 2|
\ 2*(1 + x) /
------------------------------------------
___________
/ x
x* / 1 - -----
\/ 1 + x
$$\frac{\sqrt{\frac{x}{x + 1}} \left(x + 1\right) \left(- \frac{x}{2 \left(x + 1\right)^{2}} + \frac{1}{2 x + 2}\right)}{x \sqrt{- \frac{x}{x + 1} + 1}}$$
sqrt(x/(1 + x))*(1 + x)*(1/(2 + 2*x) - x/(2*(1 + x)^2))/(x*sqrt(1 - x/(1 + x)))