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Simplificación de expresiones/ Descomposición en fracciones simples/ ((x-3)/(x^3-64)+(x-3)/(x^2+4*x+16))*(2*x^3-128)/(3-x)

¿Cómo vas a descomponer esta ((x-3)/(x^3-64)+(x-3)/(x^2+4*x+16))*(2*x^3-128)/(3-x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
/ x - 3        x - 3    \ /   3      \
|------- + -------------|*\2*x  - 128/
| 3         2           |             
\x  - 64   x  + 4*x + 16/             
--------------------------------------
                3 - x
(2x3−128)(x−3(x2+4x)+16+x−3x3−64)3−x\frac{\left(2 x^{3} - 128\right) \left(\frac{x - 3}{\left(x^{2} + 4 x\right) + 16} + \frac{x - 3}{x^{3} - 64}\right)}{3 - x} 
(((x - 3)/(x^3 - 64) + (x - 3)/(x^2 + 4*x + 16))*(2*x^3 - 128))/(3 - x)
Simplificación general [src] 
6 - 2*x
6−2x6 - 2 x 
6 - 2*x
Descomposición de una fracción [src] 
6 - 2*x
6−2x6 - 2 x 
6 - 2*x
Denominador común [src] 
6 - 2*x
6−2x6 - 2 x 
6 - 2*x
Combinatoria [src] 
6 - 2*x
6−2x6 - 2 x 
6 - 2*x
Potencias [src] 
/          3\ / -3 + x        -3 + x   \
\-128 + 2*x /*|-------- + -------------|
              |       3         2      |
              \-64 + x    16 + x  + 4*x/
----------------------------------------
                 3 - x
(2x3−128)(x−3x2+4x+16+x−3x3−64)3−x\frac{\left(2 x^{3} - 128\right) \left(\frac{x - 3}{x^{2} + 4 x + 16} + \frac{x - 3}{x^{3} - 64}\right)}{3 - x} 
(-128 + 2*x^3)*((-3 + x)/(-64 + x^3) + (-3 + x)/(16 + x^2 + 4*x))/(3 - x)
Unión de expresiones racionales [src] 
           /       3            \
2*(-3 + x)*\-48 + x  + x*(4 + x)/
---------------------------------
     (3 - x)*(16 + x*(4 + x))
2(x−3)(x3+x(x+4)−48)(3−x)(x(x+4)+16)\frac{2 \left(x - 3\right) \left(x^{3} + x \left(x + 4\right) - 48\right)}{\left(3 - x\right) \left(x \left(x + 4\right) + 16\right)} 
2*(-3 + x)*(-48 + x^3 + x*(4 + x))/((3 - x)*(16 + x*(4 + x)))
Compilar la expresión [src] 
/          3\ / -3 + x        -3 + x   \
\-128 + 2*x /*|-------- + -------------|
              |       3         2      |
              \-64 + x    16 + x  + 4*x/
----------------------------------------
                 3 - x
(2x3−128)(x−3x2+4x+16+x−3x3−64)3−x\frac{\left(2 x^{3} - 128\right) \left(\frac{x - 3}{x^{2} + 4 x + 16} + \frac{x - 3}{x^{3} - 64}\right)}{3 - x} 
(-128 + 2*x^3)*((-3 + x)/(-64 + x^3) + (-3 + x)/(16 + x^2 + 4*x))/(3 - x)
Respuesta numérica [src] 
(-128.0 + 2.0*x^3)*((-3.0 + x)/(-64.0 + x^3) + (-3.0 + x)/(16.0 + x^2 + 4.0*x))/(3.0 - x)
(-128.0 + 2.0*x^3)*((-3.0 + x)/(-64.0 + x^3) + (-3.0 + x)/(16.0 + x^2 + 4.0*x))/(3.0 - x)
Denominador racional [src] 
/          3\ //       3\                     /      2      \\
\-128 + 2*x /*\\-64 + x /*(-3 + x) + (-3 + x)*\16 + x  + 4*x//
--------------------------------------------------------------
              /       3\         /      2      \              
              \-64 + x /*(3 - x)*\16 + x  + 4*x/
(2x3−128)((x−3)(x3−64)+(x−3)(x2+4x+16))(3−x)(x3−64)(x2+4x+16)\frac{\left(2 x^{3} - 128\right) \left(\left(x - 3\right) \left(x^{3} - 64\right) + \left(x - 3\right) \left(x^{2} + 4 x + 16\right)\right)}{\left(3 - x\right) \left(x^{3} - 64\right) \left(x^{2} + 4 x + 16\right)} 
(-128 + 2*x^3)*((-64 + x^3)*(-3 + x) + (-3 + x)*(16 + x^2 + 4*x))/((-64 + x^3)*(3 - x)*(16 + x^2 + 4*x))
Parte trigonométrica [src] 
/          3\ / -3 + x        -3 + x   \
\-128 + 2*x /*|-------- + -------------|
              |       3         2      |
              \-64 + x    16 + x  + 4*x/
----------------------------------------
                 3 - x
(2x3−128)(x−3x2+4x+16+x−3x3−64)3−x\frac{\left(2 x^{3} - 128\right) \left(\frac{x - 3}{x^{2} + 4 x + 16} + \frac{x - 3}{x^{3} - 64}\right)}{3 - x} 
(-128 + 2*x^3)*((-3 + x)/(-64 + x^3) + (-3 + x)/(16 + x^2 + 4*x))/(3 - x)
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