Sr Examen
¿Cómo vas a descomponer esta 3/(2*x+2*x)+2*x-1/(x-1)-2/x expresión en fracciones?
Solución
Ha introducido
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3 1 2 --------- + 2*x - ----- - - 2*x + 2*x x - 1 x
$$\left(\left(2 x + \frac{3}{2 x + 2 x}\right) - \frac{1}{x - 1}\right) - \frac{2}{x}$$
3/(2*x + 2*x) + 2*x - 1/(x - 1) - 2/x
Descomposición de una fracción
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-1/(-1 + x) + 2*x - 5/(4*x)
$$2 x - \frac{1}{x - 1} - \frac{5}{4 x}$$
1 5 - ------ + 2*x - --- -1 + x 4*x
Simplificación general
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2
5 - 9*x + 8*x *(-1 + x)
-----------------------
4*x*(-1 + x)
$$\frac{8 x^{2} \left(x - 1\right) - 9 x + 5}{4 x \left(x - 1\right)}$$
(5 - 9*x + 8*x^2*(-1 + x))/(4*x*(-1 + x))
Parte trigonométrica
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1 5 - ------ + 2*x - --- -1 + x 4*x
$$2 x - \frac{1}{x - 1} - \frac{5}{4 x}$$
-1/(-1 + x) + 2*x - 5/(4*x)
Potencias
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1 5 - ------ + 2*x - --- -1 + x 4*x
$$2 x - \frac{1}{x - 1} - \frac{5}{4 x}$$
-1/(-1 + x) + 2*x - 5/(4*x)
Denominador común
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-5 + 9*x
2*x - -----------
2
-4*x + 4*x
$$2 x - \frac{9 x - 5}{4 x^{2} - 4 x}$$
2*x - (-5 + 9*x)/(-4*x + 4*x^2)
Compilar la expresión
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1 5 - ------ + 2*x - --- -1 + x 4*x
$$2 x - \frac{1}{x - 1} - \frac{5}{4 x}$$
-1/(-1 + x) + 2*x - 5/(4*x)
Denominador racional
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/ / 2\\
x*\-4*x + (-1 + x)*\3 + 8*x // - 8*x*(-1 + x)
---------------------------------------------
2
4*x *(-1 + x)
$$\frac{x \left(- 4 x + \left(x - 1\right) \left(8 x^{2} + 3\right)\right) - 8 x \left(x - 1\right)}{4 x^{2} \left(x - 1\right)}$$
(x*(-4*x + (-1 + x)*(3 + 8*x^2)) - 8*x*(-1 + x))/(4*x^2*(-1 + x))
Combinatoria
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2 3
5 - 9*x - 8*x + 8*x
---------------------
4*x*(-1 + x)
$$\frac{8 x^{3} - 8 x^{2} - 9 x + 5}{4 x \left(x - 1\right)}$$
(5 - 9*x - 8*x^2 + 8*x^3)/(4*x*(-1 + x))
Unión de expresiones racionales
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/ 2\
8 - 12*x + (-1 + x)*\3 + 8*x /
------------------------------
4*x*(-1 + x)
$$\frac{- 12 x + \left(x - 1\right) \left(8 x^{2} + 3\right) + 8}{4 x \left(x - 1\right)}$$
(8 - 12*x + (-1 + x)*(3 + 8*x^2))/(4*x*(-1 + x))