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

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)