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