Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
((x+1)/(2x-3))+((x-1)/(2x+3))-((2x^2-7x)/(4x^2-9))
¿Cómo vas a descomponer esta ((x+1)/(2x-3))+((x-1)/(2x+3))-((2x^2-7x)/(4x^2-9)) expresión en fracciones?
Solución
Ha introducido
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2
x + 1 x - 1 2*x - 7*x
------- + ------- - ----------
2*x - 3 2*x + 3 2
4*x - 9
$$- \frac{2 x^{2} - 7 x}{4 x^{2} - 9} + \left(\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3}\right)$$
(x + 1)/(2*x - 3) + (x - 1)/(2*x + 3) - (2*x^2 - 7*x)/(4*x^2 - 9)
Descomposición de una fracción
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1/2 + 7/(2*(-3 + 2*x))
$$\frac{1}{2} + \frac{7}{2 \left(2 x - 3\right)}$$
1 7 - + ------------ 2 2*(-3 + 2*x)
Respuesta numérica
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(-1.0 + x)/(3.0 + 2.0*x) + (1.0 + x)/(-3.0 + 2.0*x) - (2.0*x^2 - 7.0*x)/(-9.0 + 4.0*x^2)
(-1.0 + x)/(3.0 + 2.0*x) + (1.0 + x)/(-3.0 + 2.0*x) - (2.0*x^2 - 7.0*x)/(-9.0 + 4.0*x^2)
Compilar la expresión
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2
1 + x -1 + x -7*x + 2*x
-------- + ------- - -----------
-3 + 2*x 3 + 2*x 2
-9 + 4*x
$$\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3} - \frac{2 x^{2} - 7 x}{4 x^{2} - 9}$$
(1 + x)/(-3 + 2*x) + (-1 + x)/(3 + 2*x) - (-7*x + 2*x^2)/(-9 + 4*x^2)
Denominador común
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1 7 - + -------- 2 -6 + 4*x
$$\frac{1}{2} + \frac{7}{4 x - 6}$$
1/2 + 7/(-6 + 4*x)
Parte trigonométrica
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2
1 + x -1 + x -7*x + 2*x
-------- + ------- - -----------
-3 + 2*x 3 + 2*x 2
-9 + 4*x
$$\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3} - \frac{2 x^{2} - 7 x}{4 x^{2} - 9}$$
(1 + x)/(-3 + 2*x) + (-1 + x)/(3 + 2*x) - (-7*x + 2*x^2)/(-9 + 4*x^2)
Denominador racional
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/ 2\ / 2 \
\-9 + 4*x /*((1 + x)*(3 + 2*x) + (-1 + x)*(-3 + 2*x)) + (-3 + 2*x)*(3 + 2*x)*\- 2*x + 7*x/
-------------------------------------------------------------------------------------------
/ 2\
\-9 + 4*x /*(-3 + 2*x)*(3 + 2*x)
$$\frac{\left(2 x - 3\right) \left(2 x + 3\right) \left(- 2 x^{2} + 7 x\right) + \left(4 x^{2} - 9\right) \left(\left(x - 1\right) \left(2 x - 3\right) + \left(x + 1\right) \left(2 x + 3\right)\right)}{\left(2 x - 3\right) \left(2 x + 3\right) \left(4 x^{2} - 9\right)}$$
((-9 + 4*x^2)*((1 + x)*(3 + 2*x) + (-1 + x)*(-3 + 2*x)) + (-3 + 2*x)*(3 + 2*x)*(-2*x^2 + 7*x))/((-9 + 4*x^2)*(-3 + 2*x)*(3 + 2*x))
Unión de expresiones racionales
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/ 2\
\-9 + 4*x /*((1 + x)*(3 + 2*x) + (-1 + x)*(-3 + 2*x)) - x*(-7 + 2*x)*(-3 + 2*x)*(3 + 2*x)
-----------------------------------------------------------------------------------------
/ 2\
\-9 + 4*x /*(-3 + 2*x)*(3 + 2*x)
$$\frac{- x \left(2 x - 7\right) \left(2 x - 3\right) \left(2 x + 3\right) + \left(4 x^{2} - 9\right) \left(\left(x - 1\right) \left(2 x - 3\right) + \left(x + 1\right) \left(2 x + 3\right)\right)}{\left(2 x - 3\right) \left(2 x + 3\right) \left(4 x^{2} - 9\right)}$$
((-9 + 4*x^2)*((1 + x)*(3 + 2*x) + (-1 + x)*(-3 + 2*x)) - x*(-7 + 2*x)*(-3 + 2*x)*(3 + 2*x))/((-9 + 4*x^2)*(-3 + 2*x)*(3 + 2*x))
Potencias
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2
1 + x -1 + x -7*x + 2*x
-------- + ------- - -----------
-3 + 2*x 3 + 2*x 2
-9 + 4*x
$$\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3} - \frac{2 x^{2} - 7 x}{4 x^{2} - 9}$$
2
- 2*x + 7*x 1 + x -1 + x
------------ + -------- + -------
2 -3 + 2*x 3 + 2*x
-9 + 4*x
$$\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3} + \frac{- 2 x^{2} + 7 x}{4 x^{2} - 9}$$
(-2*x^2 + 7*x)/(-9 + 4*x^2) + (1 + x)/(-3 + 2*x) + (-1 + x)/(3 + 2*x)