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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x)/64-1/(8*x)-log(x-8)/64

¿Cómo vas a descomponer esta log(x)/64-1/(8*x)-log(x-8)/64 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
log(x)    1    log(x - 8)
------ - --- - ----------
  64     8*x       64
$$\left(\frac{\log{\left(x \right)}}{64} - \frac{1}{8 x}\right) - \frac{\log{\left(x - 8 \right)}}{64}$$ 
log(x)/64 - 1/(8*x) - log(x - 8)/64
Simplificación general [src] 
-8 + x*(-log(-8 + x) + log(x))
------------------------------
             64*x
$$\frac{x \left(\log{\left(x \right)} - \log{\left(x - 8 \right)}\right) - 8}{64 x}$$ 
(-8 + x*(-log(-8 + x) + log(x)))/(64*x)
Respuesta numérica [src] 
0.015625*log(x) - 0.015625*log(x - 8) - 0.125/x
0.015625*log(x) - 0.015625*log(x - 8) - 0.125/x
Potencias [src] 
   1    log(-8 + x)   log(x)
- --- - ----------- + ------
  8*x        64         64
$$\frac{\log{\left(x \right)}}{64} - \frac{\log{\left(x - 8 \right)}}{64} - \frac{1}{8 x}$$ 
-1/(8*x) - log(-8 + x)/64 + log(x)/64
Denominador racional [src] 
-4096 - 512*x*log(-8 + x) + 512*x*log(x)
----------------------------------------
                32768*x
$$\frac{512 x \log{\left(x \right)} - 512 x \log{\left(x - 8 \right)} - 4096}{32768 x}$$ 
(-4096 - 512*x*log(-8 + x) + 512*x*log(x))/(32768*x)
Parte trigonométrica [src] 
   1    log(-8 + x)   log(x)
- --- - ----------- + ------
  8*x        64         64
$$\frac{\log{\left(x \right)}}{64} - \frac{\log{\left(x - 8 \right)}}{64} - \frac{1}{8 x}$$ 
-1/(8*x) - log(-8 + x)/64 + log(x)/64
Combinatoria [src] 
-(8 + x*log(-8 + x) - x*log(x)) 
--------------------------------
              64*x
$$- \frac{- x \log{\left(x \right)} + x \log{\left(x - 8 \right)} + 8}{64 x}$$ 
-(8 + x*log(-8 + x) - x*log(x))/(64*x)
Denominador común [src] 
   1    log(-8 + x)   log(x)
- --- - ----------- + ------
  8*x        64         64
$$\frac{\log{\left(x \right)}}{64} - \frac{\log{\left(x - 8 \right)}}{64} - \frac{1}{8 x}$$ 
-1/(8*x) - log(-8 + x)/64 + log(x)/64
Abrimos la expresión [src] 
   1    log(x)   log(x - 8)
- --- + ------ - ----------
  8*x     64         64
$$\frac{\log{\left(x \right)}}{64} - \frac{\log{\left(x - 8 \right)}}{64} - \frac{1}{8 x}$$ 
-1/(8*x) + log(x)/64 - log(x - 8)/64
Compilar la expresión [src] 
   1    log(x - 8)   log(x)
- --- - ---------- + ------
  8*x       64         64
$$\frac{\log{\left(x \right)}}{64} - \frac{\log{\left(x - 8 \right)}}{64} - \frac{1}{8 x}$$ 
-1/(8*x) - log(x - 8)/64 + log(x)/64
Unión de expresiones racionales [src] 
-8 + x*log(x) - x*log(-8 + x)
-----------------------------
             64*x
$$\frac{x \log{\left(x \right)} - x \log{\left(x - 8 \right)} - 8}{64 x}$$ 
(-8 + x*log(x) - x*log(-8 + x))/(64*x)
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