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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x+9)/81-log(x)/81-1/(9*x)

¿Cómo vas a descomponer esta log(x+9)/81-log(x)/81-1/(9*x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
log(x + 9)   log(x)    1 
---------- - ------ - ---
    81         81     9*x
$$\left(- \frac{\log{\left(x \right)}}{81} + \frac{\log{\left(x + 9 \right)}}{81}\right) - \frac{1}{9 x}$$ 
log(x + 9)/81 - log(x)/81 - 1/(9*x)
Simplificación general [src] 
-9 + x*(-log(x) + log(9 + x))
-----------------------------
             81*x
$$\frac{x \left(- \log{\left(x \right)} + \log{\left(x + 9 \right)}\right) - 9}{81 x}$$ 
(-9 + x*(-log(x) + log(9 + x)))/(81*x)
Potencias [src] 
   1    log(x)   log(9 + x)
- --- - ------ + ----------
  9*x     81         81
$$- \frac{\log{\left(x \right)}}{81} + \frac{\log{\left(x + 9 \right)}}{81} - \frac{1}{9 x}$$ 
-1/(9*x) - log(x)/81 + log(9 + x)/81
Respuesta numérica [src] 
0.0123456790123457*log(x + 9) - 0.0123456790123457*log(x) - 0.111111111111111/x
0.0123456790123457*log(x + 9) - 0.0123456790123457*log(x) - 0.111111111111111/x
Abrimos la expresión [src] 
   1    log(x + 9)   log(x)
- --- + ---------- - ------
  9*x       81         81
$$- \frac{\log{\left(x \right)}}{81} + \frac{\log{\left(x + 9 \right)}}{81} - \frac{1}{9 x}$$ 
-1/(9*x) + log(x + 9)/81 - log(x)/81
Denominador racional [src] 
-81 - 9*x*log(x) + 9*x*log(9 + x)
---------------------------------
              729*x
$$\frac{- 9 x \log{\left(x \right)} + 9 x \log{\left(x + 9 \right)} - 81}{729 x}$$ 
(-81 - 9*x*log(x) + 9*x*log(9 + x))/(729*x)
Combinatoria [src] 
-9 + x*log(9 + x) - x*log(x)
----------------------------
            81*x
$$\frac{- x \log{\left(x \right)} + x \log{\left(x + 9 \right)} - 9}{81 x}$$ 
(-9 + x*log(9 + x) - x*log(x))/(81*x)
Denominador común [src] 
   1    log(x)   log(9 + x)
- --- - ------ + ----------
  9*x     81         81
$$- \frac{\log{\left(x \right)}}{81} + \frac{\log{\left(x + 9 \right)}}{81} - \frac{1}{9 x}$$ 
-1/(9*x) - log(x)/81 + log(9 + x)/81
Parte trigonométrica [src] 
   1    log(x)   log(9 + x)
- --- - ------ + ----------
  9*x     81         81
$$- \frac{\log{\left(x \right)}}{81} + \frac{\log{\left(x + 9 \right)}}{81} - \frac{1}{9 x}$$ 
-1/(9*x) - log(x)/81 + log(9 + x)/81
Compilar la expresión [src] 
   1    log(x)   log(x + 9)
- --- - ------ + ----------
  9*x     81         81
$$- \frac{\log{\left(x \right)}}{81} + \frac{\log{\left(x + 9 \right)}}{81} - \frac{1}{9 x}$$ 
-1/(9*x) - log(x)/81 + log(x + 9)/81
Unión de expresiones racionales [src] 
-9 + x*(-log(x) + log(9 + x))
-----------------------------
             81*x
$$\frac{x \left(- \log{\left(x \right)} + \log{\left(x + 9 \right)}\right) - 9}{81 x}$$ 
(-9 + x*(-log(x) + log(9 + x)))/(81*x)
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