Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
Abs((x-3)*(x+7))/(((x-3)*(x+7)))+Abs((x-6)*(x+5))/(((x-6)*(x+5)))
¿Cómo vas a descomponer esta Abs((x-3)*(x+7))/(((x-3)*(x+7)))+Abs((x-6)*(x+5))/(((x-6)*(x+5))) expresión en fracciones?
Solución
Ha introducido
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|(x - 3)*(x + 7)| |(x - 6)*(x + 5)| ----------------- + ----------------- (x - 3)*(x + 7) (x - 6)*(x + 5)
$$\frac{\left|{\left(x - 3\right) \left(x + 7\right)}\right|}{\left(x - 3\right) \left(x + 7\right)} + \frac{\left|{\left(x - 6\right) \left(x + 5\right)}\right|}{\left(x - 6\right) \left(x + 5\right)}$$
Abs((x - 3)*(x + 7))/(((x - 3)*(x + 7))) + Abs((x - 6)*(x + 5))/(((x - 6)*(x + 5)))
Simplificación general
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(-6 + x)*(5 + x)*|(-3 + x)*(7 + x)| + (-3 + x)*(7 + x)*|(-6 + x)*(5 + x)|
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(-6 + x)*(-3 + x)*(5 + x)*(7 + x)
$$\frac{\left(x - 6\right) \left(x + 5\right) \left|{\left(x - 3\right) \left(x + 7\right)}\right| + \left(x - 3\right) \left(x + 7\right) \left|{\left(x - 6\right) \left(x + 5\right)}\right|}{\left(x - 6\right) \left(x - 3\right) \left(x + 5\right) \left(x + 7\right)}$$
((-6 + x)*(5 + x)*Abs((-3 + x)*(7 + x)) + (-3 + x)*(7 + x)*Abs((-6 + x)*(5 + x)))/((-6 + x)*(-3 + x)*(5 + x)*(7 + x))
Respuesta numérica
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Abs((x - 6)*(x + 5))/((5.0 + x)*(-6.0 + x)) + Abs((x - 3)*(x + 7))/((7.0 + x)*(-3.0 + x))
Abs((x - 6)*(x + 5))/((5.0 + x)*(-6.0 + x)) + Abs((x - 3)*(x + 7))/((7.0 + x)*(-3.0 + x))
Unión de expresiones racionales
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(-6 + x)*(5 + x)*|(-3 + x)*(7 + x)| + (-3 + x)*(7 + x)*|(-6 + x)*(5 + x)|
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(-6 + x)*(-3 + x)*(5 + x)*(7 + x)
$$\frac{\left(x - 6\right) \left(x + 5\right) \left|{\left(x - 3\right) \left(x + 7\right)}\right| + \left(x - 3\right) \left(x + 7\right) \left|{\left(x - 6\right) \left(x + 5\right)}\right|}{\left(x - 6\right) \left(x - 3\right) \left(x + 5\right) \left(x + 7\right)}$$
((-6 + x)*(5 + x)*Abs((-3 + x)*(7 + x)) + (-3 + x)*(7 + x)*Abs((-6 + x)*(5 + x)))/((-6 + x)*(-3 + x)*(5 + x)*(7 + x))
Combinatoria
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| 2 | | 2| 2 | 2 | 2 | 2| | 2 | | 2|
- 30*|-21 + x + 4*x| - 21*|30 + x - x | + x *|-21 + x + 4*x| + x *|30 + x - x | - x*|-21 + x + 4*x| + 4*x*|30 + x - x |
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(-6 + x)*(-3 + x)*(5 + x)*(7 + x)
$$\frac{x^{2} \left|{- x^{2} + x + 30}\right| + x^{2} \left|{x^{2} + 4 x - 21}\right| + 4 x \left|{- x^{2} + x + 30}\right| - x \left|{x^{2} + 4 x - 21}\right| - 21 \left|{- x^{2} + x + 30}\right| - 30 \left|{x^{2} + 4 x - 21}\right|}{\left(x - 6\right) \left(x - 3\right) \left(x + 5\right) \left(x + 7\right)}$$
(-30*|-21 + x^2 + 4*x| - 21*|30 + x - x^2| + x^2*|-21 + x^2 + 4*x| + x^2*|30 + x - x^2| - x*|-21 + x^2 + 4*x| + 4*x*|30 + x - x^2|)/((-6 + x)*(-3 + x)*(5 + x)*(7 + x))
Denominador racional
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| 2 | | 2| 2 | 2 | 2 | 2| | 2 | | 2|
- 30*|-21 + x + 4*x| - 21*|30 + x - x | + x *|-21 + x + 4*x| + x *|30 + x - x | - x*|-21 + x + 4*x| + 4*x*|30 + x - x |
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(-6 + x)*(-3 + x)*(5 + x)*(7 + x)
$$\frac{x^{2} \left|{- x^{2} + x + 30}\right| + x^{2} \left|{x^{2} + 4 x - 21}\right| + 4 x \left|{- x^{2} + x + 30}\right| - x \left|{x^{2} + 4 x - 21}\right| - 21 \left|{- x^{2} + x + 30}\right| - 30 \left|{x^{2} + 4 x - 21}\right|}{\left(x - 6\right) \left(x - 3\right) \left(x + 5\right) \left(x + 7\right)}$$
(-30*|-21 + x^2 + 4*x| - 21*|30 + x - x^2| + x^2*|-21 + x^2 + 4*x| + x^2*|30 + x - x^2| - x*|-21 + x^2 + 4*x| + 4*x*|30 + x - x^2|)/((-6 + x)*(-3 + x)*(5 + x)*(7 + x))
Denominador común
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| 2 | | 2| 2 | 2 | 2 | 2| | 2 | | 2|
- 30*|-21 + x + 4*x| - 21*|30 + x - x | + x *|-21 + x + 4*x| + x *|30 + x - x | - x*|-21 + x + 4*x| + 4*x*|30 + x - x |
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4 2 3
630 + x - 99*x - 55*x + 3*x
$$\frac{x^{2} \left|{- x^{2} + x + 30}\right| + x^{2} \left|{x^{2} + 4 x - 21}\right| + 4 x \left|{- x^{2} + x + 30}\right| - x \left|{x^{2} + 4 x - 21}\right| - 21 \left|{- x^{2} + x + 30}\right| - 30 \left|{x^{2} + 4 x - 21}\right|}{x^{4} + 3 x^{3} - 55 x^{2} - 99 x + 630}$$
(-30*|-21 + x^2 + 4*x| - 21*|30 + x - x^2| + x^2*|-21 + x^2 + 4*x| + x^2*|30 + x - x^2| - x*|-21 + x^2 + 4*x| + 4*x*|30 + x - x^2|)/(630 + x^4 - 99*x - 55*x^2 + 3*x^3)