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