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Simplificación de expresiones/ Descomposición en fracciones simples/ atan((2*x-4)/4)/16+(x-2)/(64-32*x+8*x^2)

¿Cómo vas a descomponer esta atan((2*x-4)/4)/16+(x-2)/(64-32*x+8*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /2*x - 4\                   
atan|-------|                   
    \   4   /        x - 2      
------------- + ----------------
      16                       2
                64 - 32*x + 8*x
x−28x2+(64−32x)+atan⁡(2x−44)16\frac{x - 2}{8 x^{2} + \left(64 - 32 x\right)} + \frac{\operatorname{atan}{\left(\frac{2 x - 4}{4} \right)}}{16} 
atan((2*x - 4)/4)/16 + (x - 2)/(64 - 32*x + 8*x^2)
Simplificación general [src] 
           /     2      \     /     x\
-4 + 2*x + \8 + x  - 4*x/*atan|-1 + -|
                              \     2/
--------------------------------------
             /     2      \           
          16*\8 + x  - 4*x/
2x+(x2−4x+8)atan⁡(x2−1)−416(x2−4x+8)\frac{2 x + \left(x^{2} - 4 x + 8\right) \operatorname{atan}{\left(\frac{x}{2} - 1 \right)} - 4}{16 \left(x^{2} - 4 x + 8\right)} 
(-4 + 2*x + (8 + x^2 - 4*x)*atan(-1 + x/2))/(16*(8 + x^2 - 4*x))
Denominador racional [src] 
                 /     x\    2     /     x\           /     x\
-4 + 2*x + 8*atan|-1 + -| + x *atan|-1 + -| - 4*x*atan|-1 + -|
                 \     2/          \     2/           \     2/
--------------------------------------------------------------
                                       2                      
                      128 - 64*x + 16*x
x2atan⁡(x2−1)−4xatan⁡(x2−1)+2x+8atan⁡(x2−1)−416x2−64x+128\frac{x^{2} \operatorname{atan}{\left(\frac{x}{2} - 1 \right)} - 4 x \operatorname{atan}{\left(\frac{x}{2} - 1 \right)} + 2 x + 8 \operatorname{atan}{\left(\frac{x}{2} - 1 \right)} - 4}{16 x^{2} - 64 x + 128} 
(-4 + 2*x + 8*atan(-1 + x/2) + x^2*atan(-1 + x/2) - 4*x*atan(-1 + x/2))/(128 - 64*x + 16*x^2)
Parte trigonométrica [src] 
    /     x\                   
atan|-1 + -|                   
    \     2/        -2 + x     
------------ + ----------------
     16                       2
               64 - 32*x + 8*x
x−28x2−32x+64+atan⁡(x2−1)16\frac{x - 2}{8 x^{2} - 32 x + 64} + \frac{\operatorname{atan}{\left(\frac{x}{2} - 1 \right)}}{16} 
atan(-1 + x/2)/16 + (-2 + x)/(64 - 32*x + 8*x^2)
Potencias [src] 
    /     x\                   
atan|-1 + -|                   
    \     2/        -2 + x     
------------ + ----------------
     16                       2
               64 - 32*x + 8*x
x−28x2−32x+64+atan⁡(x2−1)16\frac{x - 2}{8 x^{2} - 32 x + 64} + \frac{\operatorname{atan}{\left(\frac{x}{2} - 1 \right)}}{16} 
atan(-1 + x/2)/16 + (-2 + x)/(64 - 32*x + 8*x^2)
Denominador común [src] 
    /     x\                   
atan|-1 + -|                   
    \     2/        -2 + x     
------------ + ----------------
     16                       2
               64 - 32*x + 8*x
x−28x2−32x+64+atan⁡(x2−1)16\frac{x - 2}{8 x^{2} - 32 x + 64} + \frac{\operatorname{atan}{\left(\frac{x}{2} - 1 \right)}}{16} 
atan(-1 + x/2)/16 + (-2 + x)/(64 - 32*x + 8*x^2)
Combinatoria [src] 
                 /     x\    2     /     x\           /     x\
-4 + 2*x + 8*atan|-1 + -| + x *atan|-1 + -| - 4*x*atan|-1 + -|
                 \     2/          \     2/           \     2/
--------------------------------------------------------------
                         /     2      \                       
                      16*\8 + x  - 4*x/
x2atan⁡(x2−1)−4xatan⁡(x2−1)+2x+8atan⁡(x2−1)−416(x2−4x+8)\frac{x^{2} \operatorname{atan}{\left(\frac{x}{2} - 1 \right)} - 4 x \operatorname{atan}{\left(\frac{x}{2} - 1 \right)} + 2 x + 8 \operatorname{atan}{\left(\frac{x}{2} - 1 \right)} - 4}{16 \left(x^{2} - 4 x + 8\right)} 
(-4 + 2*x + 8*atan(-1 + x/2) + x^2*atan(-1 + x/2) - 4*x*atan(-1 + x/2))/(16*(8 + x^2 - 4*x))
Compilar la expresión [src] 
    /2*x - 4\                   
atan|-------|                   
    \   4   /        -2 + x     
------------- + ----------------
      16                       2
                64 - 32*x + 8*x
x−28x2−32x+64+atan⁡(2x−44)16\frac{x - 2}{8 x^{2} - 32 x + 64} + \frac{\operatorname{atan}{\left(\frac{2 x - 4}{4} \right)}}{16} 
atan((2*x - 4)/4)/16 + (-2 + x)/(64 - 32*x + 8*x^2)
Unión de expresiones racionales [src] 
           /     2      \     /-2 + x\
-4 + 2*x + \8 + x  - 4*x/*atan|------|
                              \  2   /
--------------------------------------
             /     2      \           
          16*\8 + x  - 4*x/
2x+(x2−4x+8)atan⁡(x−22)−416(x2−4x+8)\frac{2 x + \left(x^{2} - 4 x + 8\right) \operatorname{atan}{\left(\frac{x - 2}{2} \right)} - 4}{16 \left(x^{2} - 4 x + 8\right)} 
(-4 + 2*x + (8 + x^2 - 4*x)*atan((-2 + x)/2))/(16*(8 + x^2 - 4*x))
Respuesta numérica [src] 
0.0625*atan((2*x - 4)/4) + (-2.0 + x)/(64.0 + 8.0*x^2 - 32.0*x)
0.0625*atan((2*x - 4)/4) + (-2.0 + x)/(64.0 + 8.0*x^2 - 32.0*x)
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