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Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(-x/(-1+x))*(-1+x/(-1+x))*(2/x+2/(-1+x)+(-1+x/(-1+x))/x)/(4*x)
¿Cómo vas a descomponer esta sqrt(-x/(-1+x))*(-1+x/(-1+x))*(2/x+2/(-1+x)+(-1+x/(-1+x))/x)/(4*x) expresión en fracciones?
Solución
Ha introducido
[src]
/ x \
________ | -1 + ------|
/ -x / x \ |2 2 -1 + x|
/ ------ *|-1 + ------|*|- + ------ + -----------|
\/ -1 + x \ -1 + x/ \x -1 + x x /
-----------------------------------------------------
4*x
$$\frac{\sqrt{\frac{\left(-1\right) x}{x - 1}} \left(\frac{x}{x - 1} - 1\right) \left(\left(\frac{2}{x - 1} + \frac{2}{x}\right) + \frac{\frac{x}{x - 1} - 1}{x}\right)}{4 x}$$
((sqrt((-x)/(-1 + x))*(-1 + x/(-1 + x)))*(2/x + 2/(-1 + x) + (-1 + x/(-1 + x))/x))/((4*x))
Simplificación general
[src]
________
/ -x
/ ------ *(-1/4 + x)
\/ -1 + x
-----------------------
2 2
x *(-1 + x)
$$\frac{\sqrt{- \frac{x}{x - 1}} \left(x - \frac{1}{4}\right)}{x^{2} \left(x - 1\right)^{2}}$$
sqrt(-x/(-1 + x))*(-1/4 + x)/(x^2*(-1 + x)^2)
Respuesta numérica
[src]
0.25*(-x/(-1.0 + x))^0.5*(-1.0 + x/(-1.0 + x))*(2.0/x + 2.0/(-1.0 + x) + (-1.0 + x/(-1.0 + x))/x)/x
0.25*(-x/(-1.0 + x))^0.5*(-1.0 + x/(-1.0 + x))*(2.0/x + 2.0/(-1.0 + x) + (-1.0 + x/(-1.0 + x))/x)/x
Unión de expresiones racionales
[src]
________
/ -x
/ ------ *(-1 + 4*x)
\/ -1 + x
-----------------------
2 2
4*x *(-1 + x)
$$\frac{\sqrt{- \frac{x}{x - 1}} \left(4 x - 1\right)}{4 x^{2} \left(x - 1\right)^{2}}$$
sqrt(-x/(-1 + x))*(-1 + 4*x)/(4*x^2*(-1 + x)^2)
Compilar la expresión
[src]
/ x \
________ | -1 + ------|
/ -x / x \ |2 2 -1 + x|
/ ------ *|-1 + ------|*|- + ------ + -----------|
\/ -1 + x \ -1 + x/ \x -1 + x x /
-----------------------------------------------------
4*x
$$\frac{\sqrt{- \frac{x}{x - 1}} \left(\frac{x}{x - 1} - 1\right) \left(\frac{2}{x - 1} + \frac{\frac{x}{x - 1} - 1}{x} + \frac{2}{x}\right)}{4 x}$$
sqrt(-x/(-1 + x))*(-1 + x/(-1 + x))*(2/x + 2/(-1 + x) + (-1 + x/(-1 + x))/x)/(4*x)
Parte trigonométrica
[src]
/ x \
________ | -1 + ------|
/ -x / x \ |2 2 -1 + x|
/ ------ *|-1 + ------|*|- + ------ + -----------|
\/ -1 + x \ -1 + x/ \x -1 + x x /
-----------------------------------------------------
4*x
$$\frac{\sqrt{- \frac{x}{x - 1}} \left(\frac{x}{x - 1} - 1\right) \left(\frac{2}{x - 1} + \frac{\frac{x}{x - 1} - 1}{x} + \frac{2}{x}\right)}{4 x}$$
sqrt(-x/(-1 + x))*(-1 + x/(-1 + x))*(2/x + 2/(-1 + x) + (-1 + x/(-1 + x))/x)/(4*x)
Denominador racional
[src]
________ ________
/ -x / -x
- / ------ + 4*x* / ------
\/ -1 + x \/ -1 + x
---------------------------------
2 2
4*x *(-1 + x)
$$\frac{4 x \sqrt{- \frac{x}{x - 1}} - \sqrt{- \frac{x}{x - 1}}}{4 x^{2} \left(x - 1\right)^{2}}$$
(-sqrt(-x/(-1 + x)) + 4*x*sqrt(-x/(-1 + x)))/(4*x^2*(-1 + x)^2)
Combinatoria
[src]
________
/ -x
/ ------ *(-1 + 4*x)
\/ -1 + x
-----------------------
2 2
4*x *(-1 + x)
$$\frac{\sqrt{- \frac{x}{x - 1}} \left(4 x - 1\right)}{4 x^{2} \left(x - 1\right)^{2}}$$
sqrt(-x/(-1 + x))*(-1 + 4*x)/(4*x^2*(-1 + x)^2)
Denominador común
[src]
________ ________
/ -x / -x
- / ------ + 4*x* / ------
\/ -1 + x \/ -1 + x
---------------------------------
3 2 4
- 8*x + 4*x + 4*x
$$\frac{4 x \sqrt{- \frac{x}{x - 1}} - \sqrt{- \frac{x}{x - 1}}}{4 x^{4} - 8 x^{3} + 4 x^{2}}$$
(-sqrt(-x/(-1 + x)) + 4*x*sqrt(-x/(-1 + x)))/(-8*x^3 + 4*x^2 + 4*x^4)
Potencias
[src]
/ x \
________ | -1 + ------|
/ -x / x \ |2 2 -1 + x|
/ ------ *|-1 + ------|*|- + ------ + -----------|
\/ -1 + x \ -1 + x/ \x -1 + x x /
-----------------------------------------------------
4*x
$$\frac{\sqrt{- \frac{x}{x - 1}} \left(\frac{x}{x - 1} - 1\right) \left(\frac{2}{x - 1} + \frac{\frac{x}{x - 1} - 1}{x} + \frac{2}{x}\right)}{4 x}$$
sqrt(-x/(-1 + x))*(-1 + x/(-1 + x))*(2/x + 2/(-1 + x) + (-1 + x/(-1 + x))/x)/(4*x)