Sr Examen
¿Cómo vas a descomponer esta (9a/a+3)-3a1/(a*x-1)-1/(a*x+1) expresión en fracciones?
Solución
Ha introducido
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9*a 3*a1 1 --- + 3 - ------- - ------- a a*x - 1 a*x + 1
$$\left(- \frac{3 a_{1}}{a x - 1} + \left(3 + \frac{9 a}{a}\right)\right) - \frac{1}{a x + 1}$$
(9*a)/a + 3 - 3*a1/(a*x - 1) - 1/(a*x + 1)
Simplificación general
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2 2
-11 - 3*a1 - a*x + 12*a *x - 3*a*a1*x
--------------------------------------
2 2
-1 + a *x
$$\frac{12 a^{2} x^{2} - 3 a a_{1} x - a x - 3 a_{1} - 11}{a^{2} x^{2} - 1}$$
(-11 - 3*a1 - a*x + 12*a^2*x^2 - 3*a*a1*x)/(-1 + a^2*x^2)
Respuesta numérica
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12.0 - 1/(1.0 + a*x) - 3.0*a1/(-1.0 + a*x)
12.0 - 1/(1.0 + a*x) - 3.0*a1/(-1.0 + a*x)
Unión de expresiones racionales
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1 - a*x + 3*(1 + a*x)*(-4 - a1 + 4*a*x)
---------------------------------------
(1 + a*x)*(-1 + a*x)
$$\frac{- a x + 3 \left(a x + 1\right) \left(4 a x - a_{1} - 4\right) + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$
(1 - a*x + 3*(1 + a*x)*(-4 - a1 + 4*a*x))/((1 + a*x)*(-1 + a*x))
Parte trigonométrica
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1 3*a1
12 - ------- - --------
1 + a*x -1 + a*x
$$- \frac{3 a_{1}}{a x - 1} + 12 - \frac{1}{a x + 1}$$
12 - 1/(1 + a*x) - 3*a1/(-1 + a*x)
Combinatoria
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2 2
-11 - 3*a1 - a*x + 12*a *x - 3*a*a1*x
--------------------------------------
(1 + a*x)*(-1 + a*x)
$$\frac{12 a^{2} x^{2} - 3 a a_{1} x - a x - 3 a_{1} - 11}{\left(a x - 1\right) \left(a x + 1\right)}$$
(-11 - 3*a1 - a*x + 12*a^2*x^2 - 3*a*a1*x)/((1 + a*x)*(-1 + a*x))
Denominador racional
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(1 + a*x)*(-3*a*a1 + 12*a*(-1 + a*x)) - a*(-1 + a*x)
----------------------------------------------------
a*(1 + a*x)*(-1 + a*x)
$$\frac{- a \left(a x - 1\right) + \left(- 3 a a_{1} + 12 a \left(a x - 1\right)\right) \left(a x + 1\right)}{a \left(a x - 1\right) \left(a x + 1\right)}$$
((1 + a*x)*(-3*a*a1 + 12*a*(-1 + a*x)) - a*(-1 + a*x))/(a*(1 + a*x)*(-1 + a*x))
Potencias
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1 3*a1
12 - ------- - --------
1 + a*x -1 + a*x
$$- \frac{3 a_{1}}{a x - 1} + 12 - \frac{1}{a x + 1}$$
12 - 1/(1 + a*x) - 3*a1/(-1 + a*x)
Compilar la expresión
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1 3*a1
12 - ------- - --------
1 + a*x -1 + a*x
$$- \frac{3 a_{1}}{a x - 1} + 12 - \frac{1}{a x + 1}$$
12 - 1/(1 + a*x) - 3*a1/(-1 + a*x)
Denominador común
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-1 + 3*a1 + a*x + 3*a*a1*x
12 - --------------------------
2 2
-1 + a *x
$$12 - \frac{3 a a_{1} x + a x + 3 a_{1} - 1}{a^{2} x^{2} - 1}$$
12 - (-1 + 3*a1 + a*x + 3*a*a1*x)/(-1 + a^2*x^2)