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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?

Expresión a simplificar:

Solución

Ha introducido [src] 
         1          8                1    
2*x + -------- - -------- - 2*x - --------
             2          2                2
      (x - 3)    (x - 9)          (x + 3)
(−2x+((2x+1(x−3)2)−8(x−9)2))−1(x+3)2\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)
−1(x+3)2+1(x−3)2−8(x−9)2- \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
−1(x+3)2+1(x−3)2−8(x−9)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 [src] 
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)
−1(x+3)2+1(x−3)2−8(x−9)2- \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)
−4(2x4−3x3+18x2−243x+162)(x−9)2(x−3)2(x+3)2- \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 [src] 
    1          1           8    
--------- - -------- - ---------
        2          2           2
(-3 + x)    (3 + x)    (-9 + x)
−1(x+3)2+1(x−3)2−8(x−9)2- \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
−8x4−12x3+72x2−972x+648x6−18x5+63x4+324x3−1377x2−1458x+6561- \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)
−(x−9)2(x−3)2+(x+3)2(−2x(x−9)2(x−3)2+(x−9)2(2x(x−3)2+1)−8(x−3)2)(x−9)2(x−3)2(x+3)2\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)
−1(x+3)2+1(x−3)2−8(x−9)2- \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)
−(x−9)2(x−3)2+(x+3)2(−2x(x−9)2(x−3)2+(x−9)2(2x(x−3)2+1)−8(x−3)2)(x−9)2(x−3)2(x+3)2\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)
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