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Simplificación de expresiones/ Descomposición en fracciones simples/ log((4-sqrt(2))/(4+sqrt(2)))/(4*sqrt(2))

¿Cómo vas a descomponer esta log((4-sqrt(2))/(4+sqrt(2)))/(4*sqrt(2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /      ___\
   |4 - \/ 2 |
log|---------|
   |      ___|
   \4 + \/ 2 /
--------------
       ___    
   4*\/ 2
$$\frac{\log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{4 \sqrt{2}}$$ 
log((4 - sqrt(2))/(4 + sqrt(2)))/((4*sqrt(2)))
Simplificación general [src] 
   /               ___\
   |             \/ 2 |
   |             -----|
   |               8  |
   |/        ___\     |
   ||9   4*\/ 2 |     |
log||- - -------|     |
   \\7      7   /     /
$$\log{\left(\left(\frac{9}{7} - \frac{4 \sqrt{2}}{7}\right)^{\frac{\sqrt{2}}{8}} \right)}$$ 
log((9/7 - 4*sqrt(2)/7)^(sqrt(2)/8))
Parte trigonométrica [src] 
         /      ___\
  ___    |4 - \/ 2 |
\/ 2 *log|---------|
         |      ___|
         \4 + \/ 2 /
--------------------
         8
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{8}$$ 
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/8
Combinatoria [src] 
  ___ /     /      ___\      /      ___\\
\/ 2 *\- log\4 + \/ 2 / + log\4 - \/ 2 //
-----------------------------------------
                    8
$$\frac{\sqrt{2} \left(- \log{\left(\sqrt{2} + 4 \right)} + \log{\left(4 - \sqrt{2} \right)}\right)}{8}$$ 
sqrt(2)*(-log(4 + sqrt(2)) + log(4 - sqrt(2)))/8
Unión de expresiones racionales [src] 
         /      ___\
  ___    |4 - \/ 2 |
\/ 2 *log|---------|
         |      ___|
         \4 + \/ 2 /
--------------------
         8
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{8}$$ 
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/8
Denominador común [src] 
    ___    /      ___\     ___    /      ___\
  \/ 2 *log\4 + \/ 2 /   \/ 2 *log\4 - \/ 2 /
- -------------------- + --------------------
           8                      8
$$- \frac{\sqrt{2} \log{\left(\sqrt{2} + 4 \right)}}{8} + \frac{\sqrt{2} \log{\left(4 - \sqrt{2} \right)}}{8}$$ 
-sqrt(2)*log(4 + sqrt(2))/8 + sqrt(2)*log(4 - sqrt(2))/8
Denominador racional [src] 
         /        ___\
  ___    |9 - 4*\/ 2 |
\/ 2 *log|-----------|
         \     7     /
----------------------
          8
$$\frac{\sqrt{2} \log{\left(\frac{9 - 4 \sqrt{2}}{7} \right)}}{8}$$ 
sqrt(2)*log((9 - 4*sqrt(2))/7)/8
Abrimos la expresión [src] 
         /      ___\
  ___    |4 - \/ 2 |
\/ 2 *log|---------|
         |      ___|
         \4 + \/ 2 /
--------------------
         8
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{8}$$ 
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/8
Respuesta numérica [src] 
-0.130637614345120
-0.130637614345120
Potencias [src] 
         /      ___\
  ___    |4 - \/ 2 |
\/ 2 *log|---------|
         |      ___|
         \4 + \/ 2 /
--------------------
         8
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{8}$$ 
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/8
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