Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
2*x+1/(x-3)^2-8/(x-9)^2-2*x-1/(x+3)^2
¿Cómo vas a descomponer esta 2*x+1/(x-3)^2-8/(x-9)^2-2*x-1/(x+3)^2 expresión en fracciones?
Solución
Ha introducido
[src]
1 8 1
2*x + -------- - -------- - 2*x - --------
2 2 2
(x - 3) (x - 9) (x + 3)
$$\left(- 2 x + \left(\left(2 x + \frac{1}{\left(x - 3\right)^{2}}\right) - \frac{8}{\left(x - 9\right)^{2}}\right)\right) - \frac{1}{\left(x + 3\right)^{2}}$$
2*x + 1/((x - 3)^2) - 8/(x - 9)^2 - 2*x - 1/(x + 3)^2
Simplificación general
[src]
1 1 8
--------- - -------- - ---------
2 2 2
(-3 + x) (3 + x) (-9 + x)
$$- \frac{1}{\left(x + 3\right)^{2}} + \frac{1}{\left(x - 3\right)^{2}} - \frac{8}{\left(x - 9\right)^{2}}$$
(-3 + x)^(-2) - 1/(3 + x)^2 - 8/(-9 + x)^2
Descomposición de una fracción
[src]
(-3 + x)^(-2) - 1/(3 + x)^2 - 8/(-9 + x)^2
$$- \frac{1}{\left(x + 3\right)^{2}} + \frac{1}{\left(x - 3\right)^{2}} - \frac{8}{\left(x - 9\right)^{2}}$$
1 1 8
--------- - -------- - ---------
2 2 2
(-3 + x) (3 + x) (-9 + x)
Respuesta numérica
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0.111111111111111/(-1 + 0.333333333333333*x)^2 - 0.0987654320987654/(-1 + 0.111111111111111*x)^2 - 0.111111111111111/(1 + 0.333333333333333*x)^2
0.111111111111111/(-1 + 0.333333333333333*x)^2 - 0.0987654320987654/(-1 + 0.111111111111111*x)^2 - 0.111111111111111/(1 + 0.333333333333333*x)^2
Parte trigonométrica
[src]
1 1 8
--------- - -------- - ---------
2 2 2
(-3 + x) (3 + x) (-9 + x)
$$- \frac{1}{\left(x + 3\right)^{2}} + \frac{1}{\left(x - 3\right)^{2}} - \frac{8}{\left(x - 9\right)^{2}}$$
(-3 + x)^(-2) - 1/(3 + x)^2 - 8/(-9 + x)^2
Combinatoria
[src]
/ 3 4 2\
-4*\162 - 243*x - 3*x + 2*x + 18*x /
--------------------------------------
2 2 2
(-9 + x) *(-3 + x) *(3 + x)
$$- \frac{4 \left(2 x^{4} - 3 x^{3} + 18 x^{2} - 243 x + 162\right)}{\left(x - 9\right)^{2} \left(x - 3\right)^{2} \left(x + 3\right)^{2}}$$
-4*(162 - 243*x - 3*x^3 + 2*x^4 + 18*x^2)/((-9 + x)^2*(-3 + x)^2*(3 + x)^2)
Potencias
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1 1 8
--------- - -------- - ---------
2 2 2
(-3 + x) (3 + x) (-9 + x)
$$- \frac{1}{\left(x + 3\right)^{2}} + \frac{1}{\left(x - 3\right)^{2}} - \frac{8}{\left(x - 9\right)^{2}}$$
(-3 + x)^(-2) - 1/(3 + x)^2 - 8/(-9 + x)^2
Denominador común
[src]
/ 3 4 2\
-\648 - 972*x - 12*x + 8*x + 72*x /
-----------------------------------------------------
6 2 5 4 3
6561 + x - 1458*x - 1377*x - 18*x + 63*x + 324*x
$$- \frac{8 x^{4} - 12 x^{3} + 72 x^{2} - 972 x + 648}{x^{6} - 18 x^{5} + 63 x^{4} + 324 x^{3} - 1377 x^{2} - 1458 x + 6561}$$
-(648 - 972*x - 12*x^3 + 8*x^4 + 72*x^2)/(6561 + x^6 - 1458*x - 1377*x^2 - 18*x^5 + 63*x^4 + 324*x^3)
Denominador racional
[src]
2 / 2 2 / 2\ 2 2\ 2 2
(3 + x) *\- 8*(-3 + x) + (-9 + x) *\1 + 2*x*(-3 + x) / - 2*x*(-9 + x) *(-3 + x) / - (-9 + x) *(-3 + x)
--------------------------------------------------------------------------------------------------------
2 2 2
(-9 + x) *(-3 + x) *(3 + x)
$$\frac{- \left(x - 9\right)^{2} \left(x - 3\right)^{2} + \left(x + 3\right)^{2} \left(- 2 x \left(x - 9\right)^{2} \left(x - 3\right)^{2} + \left(x - 9\right)^{2} \left(2 x \left(x - 3\right)^{2} + 1\right) - 8 \left(x - 3\right)^{2}\right)}{\left(x - 9\right)^{2} \left(x - 3\right)^{2} \left(x + 3\right)^{2}}$$
((3 + x)^2*(-8*(-3 + x)^2 + (-9 + x)^2*(1 + 2*x*(-3 + x)^2) - 2*x*(-9 + x)^2*(-3 + x)^2) - (-9 + x)^2*(-3 + x)^2)/((-9 + x)^2*(-3 + x)^2*(3 + x)^2)
Compilar la expresión
[src]
1 1 8
--------- - -------- - ---------
2 2 2
(-3 + x) (3 + x) (-9 + x)
$$- \frac{1}{\left(x + 3\right)^{2}} + \frac{1}{\left(x - 3\right)^{2}} - \frac{8}{\left(x - 9\right)^{2}}$$
(-3 + x)^(-2) - 1/(3 + x)^2 - 8/(-9 + x)^2
Unión de expresiones racionales
[src]
2 / 2 2 / 2\ 2 2\ 2 2
(3 + x) *\- 8*(-3 + x) + (-9 + x) *\1 + 2*x*(-3 + x) / - 2*x*(-9 + x) *(-3 + x) / - (-9 + x) *(-3 + x)
--------------------------------------------------------------------------------------------------------
2 2 2
(-9 + x) *(-3 + x) *(3 + x)
$$\frac{- \left(x - 9\right)^{2} \left(x - 3\right)^{2} + \left(x + 3\right)^{2} \left(- 2 x \left(x - 9\right)^{2} \left(x - 3\right)^{2} + \left(x - 9\right)^{2} \left(2 x \left(x - 3\right)^{2} + 1\right) - 8 \left(x - 3\right)^{2}\right)}{\left(x - 9\right)^{2} \left(x - 3\right)^{2} \left(x + 3\right)^{2}}$$
((3 + x)^2*(-8*(-3 + x)^2 + (-9 + x)^2*(1 + 2*x*(-3 + x)^2) - 2*x*(-9 + x)^2*(-3 + x)^2) - (-9 + x)^2*(-3 + x)^2)/((-9 + x)^2*(-3 + x)^2*(3 + x)^2)