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