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