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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x)^5100+2*log(x)^(101/2)/(a*x-1)-1/(a*x+1)

¿Cómo vas a descomponer esta log(x)^5100+2*log(x)^(101/2)/(a*x-1)-1/(a*x+1) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                  101/2             
   5100      2*log     (x)      1   
log    (x) + ------------- - -------
                a*x - 1      a*x + 1
$$\left(\log{\left(x \right)}^{5100} + \frac{2 \log{\left(x \right)}^{\frac{101}{2}}}{a x - 1}\right) - \frac{1}{a x + 1}$$ 
log(x)^5100 + (2*log(x)^(101/2))/(a*x - 1) - 1/(a*x + 1)
Simplificación general [src] 
                            101/2   
   5100         1      2*log     (x)
log    (x) - ------- + -------------
             1 + a*x      -1 + a*x
$$\log{\left(x \right)}^{5100} - \frac{1}{a x + 1} + \frac{2 \log{\left(x \right)}^{\frac{101}{2}}}{a x - 1}$$ 
log(x)^5100 - 1/(1 + a*x) + 2*log(x)^(101/2)/(-1 + a*x)
Parte trigonométrica [src] 
                            101/2   
   5100         1      2*log     (x)
log    (x) - ------- + -------------
             1 + a*x      -1 + a*x
$$\log{\left(x \right)}^{5100} - \frac{1}{a x + 1} + \frac{2 \log{\left(x \right)}^{\frac{101}{2}}}{a x - 1}$$ 
log(x)^5100 - 1/(1 + a*x) + 2*log(x)^(101/2)/(-1 + a*x)
Respuesta numérica [src] 
log(x)^5100 - 1/(1.0 + a*x) + 2.0*log(x)^50.5/(-1.0 + a*x)
log(x)^5100 - 1/(1.0 + a*x) + 2.0*log(x)^50.5/(-1.0 + a*x)
Potencias [src] 
                            101/2   
   5100         1      2*log     (x)
log    (x) - ------- + -------------
             1 + a*x      -1 + a*x
$$\log{\left(x \right)}^{5100} - \frac{1}{a x + 1} + \frac{2 \log{\left(x \right)}^{\frac{101}{2}}}{a x - 1}$$ 
log(x)^5100 - 1/(1 + a*x) + 2*log(x)^(101/2)/(-1 + a*x)
Denominador común [src] 
                      101/2                     101/2   
   5100      1 + 2*log     (x) - a*x + 2*a*x*log     (x)
log    (x) + -------------------------------------------
                                    2  2                
                              -1 + a *x
$$\log{\left(x \right)}^{5100} + \frac{2 a x \log{\left(x \right)}^{\frac{101}{2}} - a x + 2 \log{\left(x \right)}^{\frac{101}{2}} + 1}{a^{2} x^{2} - 1}$$ 
log(x)^5100 + (1 + 2*log(x)^(101/2) - a*x + 2*a*x*log(x)^(101/2))/(-1 + a^2*x^2)
Unión de expresiones racionales [src] 
              /     101/2         5100              \      
1 + (1 + a*x)*\2*log     (x) + log    (x)*(-1 + a*x)/ - a*x
-----------------------------------------------------------
                    (1 + a*x)*(-1 + a*x)
$$\frac{- a x + \left(a x + 1\right) \left(\left(a x - 1\right) \log{\left(x \right)}^{5100} + 2 \log{\left(x \right)}^{\frac{101}{2}}\right) + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$ 
(1 + (1 + a*x)*(2*log(x)^(101/2) + log(x)^5100*(-1 + a*x)) - a*x)/((1 + a*x)*(-1 + a*x))
Compilar la expresión [src] 
                            101/2   
   5100         1      2*log     (x)
log    (x) - ------- + -------------
             1 + a*x      -1 + a*x
$$\log{\left(x \right)}^{5100} - \frac{1}{a x + 1} + \frac{2 \log{\left(x \right)}^{\frac{101}{2}}}{a x - 1}$$ 
log(x)^5100 - 1/(1 + a*x) + 2*log(x)^(101/2)/(-1 + a*x)
Denominador racional [src] 
              /     101/2         5100              \      
1 + (1 + a*x)*\2*log     (x) + log    (x)*(-1 + a*x)/ - a*x
-----------------------------------------------------------
                    (1 + a*x)*(-1 + a*x)
$$\frac{- a x + \left(a x + 1\right) \left(\left(a x - 1\right) \log{\left(x \right)}^{5100} + 2 \log{\left(x \right)}^{\frac{101}{2}}\right) + 1}{\left(a x - 1\right) \left(a x + 1\right)}$$ 
(1 + (1 + a*x)*(2*log(x)^(101/2) + log(x)^5100*(-1 + a*x)) - a*x)/((1 + a*x)*(-1 + a*x))
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