Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(a)/(x-48*sqrt(x))/2*sqrt(a)/(48*sqrt(x)-x)
¿Cómo vas a descomponer esta sqrt(a)/(x-48*sqrt(x))/2*sqrt(a)/(48*sqrt(x)-x) expresión en fracciones?
Solución
Ha introducido
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/ ___ \
| \/ a |
|------------|
| ___|
\x - 48*\/ x / ___
--------------*\/ a
2
--------------------
___
48*\/ x - x
$$\frac{\sqrt{a} \frac{\sqrt{a} \frac{1}{- 48 \sqrt{x} + x}}{2}}{48 \sqrt{x} - x}$$
(((sqrt(a)/(x - 48*sqrt(x)))/2)*sqrt(a))/(48*sqrt(x) - x)
Simplificación general
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-a
------------------
2
/ ___\
2*\-x + 48*\/ x /
$$- \frac{a}{2 \left(48 \sqrt{x} - x\right)^{2}}$$
-a/(2*(-x + 48*sqrt(x))^2)
Denominador común
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-a
--------------------------
3/2 2
- 192*x + 2*x + 4608*x
$$- \frac{a}{- 192 x^{\frac{3}{2}} + 2 x^{2} + 4608 x}$$
-a/(-192*x^(3/2) + 2*x^2 + 4608*x)
Denominador racional
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3/2 2 -4608*a*x - 192*a*x - 2*a*x ------------------------------- / 2 \ / 2\ \x - 2304*x/*\-9216*x + 4*x /
$$\frac{- 192 a x^{\frac{3}{2}} - 2 a x^{2} - 4608 a x}{\left(x^{2} - 2304 x\right) \left(4 x^{2} - 9216 x\right)}$$
(-4608*a*x - 192*a*x^(3/2) - 2*a*x^2)/((x^2 - 2304*x)*(-9216*x + 4*x^2))
Potencias
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a -------------------------------- / ___\ / ___\ 2*\x - 48*\/ x /*\-x + 48*\/ x /
$$\frac{a}{2 \left(- 48 \sqrt{x} + x\right) \left(48 \sqrt{x} - x\right)}$$
-a
------------------
2
/ ___\
2*\-x + 48*\/ x /
$$- \frac{a}{2 \left(48 \sqrt{x} - x\right)^{2}}$$
-a/(2*(-x + 48*sqrt(x))^2)
Respuesta numérica
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0.5*a^1.0/((x - 48.0*x^0.5)*(-x + 48.0*x^0.5))
0.5*a^1.0/((x - 48.0*x^0.5)*(-x + 48.0*x^0.5))
Combinatoria
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-a
-----------------
2
/ ___\
2*\x - 48*\/ x /
$$- \frac{a}{2 \left(- 48 \sqrt{x} + x\right)^{2}}$$
-a/(2*(x - 48*sqrt(x))^2)
Compilar la expresión
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a -------------------------------- / ___\ / ___\ 2*\x - 48*\/ x /*\-x + 48*\/ x /
$$\frac{a}{2 \left(- 48 \sqrt{x} + x\right) \left(48 \sqrt{x} - x\right)}$$
a/(2*(x - 48*sqrt(x))*(-x + 48*sqrt(x)))
Unión de expresiones racionales
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a -------------------------------- / ___\ / ___\ 2*\x - 48*\/ x /*\-x + 48*\/ x /
$$\frac{a}{2 \left(- 48 \sqrt{x} + x\right) \left(48 \sqrt{x} - x\right)}$$
a/(2*(x - 48*sqrt(x))*(-x + 48*sqrt(x)))
Parte trigonométrica
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a -------------------------------- / ___\ / ___\ 2*\x - 48*\/ x /*\-x + 48*\/ x /
$$\frac{a}{2 \left(- 48 \sqrt{x} + x\right) \left(48 \sqrt{x} - x\right)}$$
a/(2*(x - 48*sqrt(x))*(-x + 48*sqrt(x)))