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Simplificación de expresiones/ Descomposición en fracciones simples/ log((6*x-2*sqrt(6))/(2*sqrt(6)+6*x))/(2*sqrt(6))

¿Cómo vas a descomponer esta log((6*x-2*sqrt(6))/(2*sqrt(6)+6*x))/(2*sqrt(6)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ___\
   |6*x - 2*\/ 6 |
log|-------------|
   |    ___      |
   \2*\/ 6  + 6*x/
------------------
         ___      
     2*\/ 6
log⁡(6x−266x+26)26\frac{\log{\left(\frac{6 x - 2 \sqrt{6}}{6 x + 2 \sqrt{6}} \right)}}{2 \sqrt{6}} 
log((6*x - 2*sqrt(6))/(2*sqrt(6) + 6*x))/((2*sqrt(6)))
Descomposición de una fracción [src] 
sqrt(6)*log(-2*sqrt(6)/(2*sqrt(6) + 6*x) + 6*x/(2*sqrt(6) + 6*x))/12
6log⁡(6x6x+26−266x+26)12\frac{\sqrt{6} \log{\left(\frac{6 x}{6 x + 2 \sqrt{6}} - \frac{2 \sqrt{6}}{6 x + 2 \sqrt{6}} \right)}}{12} 
         /         ___                   \
  ___    |     2*\/ 6            6*x     |
\/ 6 *log|- ------------- + -------------|
         |      ___             ___      |
         \  2*\/ 6  + 6*x   2*\/ 6  + 6*x/
------------------------------------------
                    12
Simplificación general [src] 
         /    ___      \
  ___    |- \/ 6  + 3*x|
\/ 6 *log|-------------|
         |   ___       |
         \ \/ 6  + 3*x /
------------------------
           12
6log⁡(3x−63x+6)12\frac{\sqrt{6} \log{\left(\frac{3 x - \sqrt{6}}{3 x + \sqrt{6}} \right)}}{12} 
sqrt(6)*log((-sqrt(6) + 3*x)/(sqrt(6) + 3*x))/12
Respuesta numérica [src] 
0.204124145231932*log((6*x - 2*sqrt(6))/(2*sqrt(6) + 6*x))
0.204124145231932*log((6*x - 2*sqrt(6))/(2*sqrt(6) + 6*x))
Parte trigonométrica [src] 
         /      ___      \
  ___    |- 2*\/ 6  + 6*x|
\/ 6 *log|---------------|
         |     ___       |
         \ 2*\/ 6  + 6*x /
--------------------------
            12
6log⁡(6x−266x+26)12\frac{\sqrt{6} \log{\left(\frac{6 x - 2 \sqrt{6}}{6 x + 2 \sqrt{6}} \right)}}{12} 
sqrt(6)*log((-2*sqrt(6) + 6*x)/(2*sqrt(6) + 6*x))/12
Denominador racional [src] 
         /       2         ___\
  ___    |2 + 3*x  - 2*x*\/ 6 |
\/ 6 *log|--------------------|
         |             2      |
         \     -2 + 3*x       /
-------------------------------
               12
6log⁡(3x2−26x+23x2−2)12\frac{\sqrt{6} \log{\left(\frac{3 x^{2} - 2 \sqrt{6} x + 2}{3 x^{2} - 2} \right)}}{12} 
sqrt(6)*log((2 + 3*x^2 - 2*x*sqrt(6))/(-2 + 3*x^2))/12
Unión de expresiones racionales [src] 
         /    ___      \
  ___    |- \/ 6  + 3*x|
\/ 6 *log|-------------|
         |   ___       |
         \ \/ 6  + 3*x /
------------------------
           12
6log⁡(3x−63x+6)12\frac{\sqrt{6} \log{\left(\frac{3 x - \sqrt{6}}{3 x + \sqrt{6}} \right)}}{12} 
sqrt(6)*log((-sqrt(6) + 3*x)/(sqrt(6) + 3*x))/12
Combinatoria [src] 
         /         ___                   \
  ___    |     2*\/ 6            6*x     |
\/ 6 *log|- ------------- + -------------|
         |      ___             ___      |
         \  2*\/ 6  + 6*x   2*\/ 6  + 6*x/
------------------------------------------
                    12
6log⁡(6x6x+26−266x+26)12\frac{\sqrt{6} \log{\left(\frac{6 x}{6 x + 2 \sqrt{6}} - \frac{2 \sqrt{6}}{6 x + 2 \sqrt{6}} \right)}}{12} 
sqrt(6)*log(-2*sqrt(6)/(2*sqrt(6) + 6*x) + 6*x/(2*sqrt(6) + 6*x))/12
Denominador común [src] 
         /       ___                 \
  ___    |     \/ 6           3*x    |
\/ 6 *log|- ----------- + -----------|
         |    ___           ___      |
         \  \/ 6  + 3*x   \/ 6  + 3*x/
--------------------------------------
                  12
6log⁡(3x3x+6−63x+6)12\frac{\sqrt{6} \log{\left(\frac{3 x}{3 x + \sqrt{6}} - \frac{\sqrt{6}}{3 x + \sqrt{6}} \right)}}{12} 
sqrt(6)*log(-sqrt(6)/(sqrt(6) + 3*x) + 3*x/(sqrt(6) + 3*x))/12
Compilar la expresión [src] 
         /          ___\
  ___    |6*x - 2*\/ 6 |
\/ 6 *log|-------------|
         |    ___      |
         \2*\/ 6  + 6*x/
------------------------
           12
6log⁡(6x−266x+26)12\frac{\sqrt{6} \log{\left(\frac{6 x - 2 \sqrt{6}}{6 x + 2 \sqrt{6}} \right)}}{12} 
sqrt(6)*log((6*x - 2*sqrt(6))/(2*sqrt(6) + 6*x))/12
Abrimos la expresión [src] 
         /          ___\
  ___    |6*x - 2*\/ 6 |
\/ 6 *log|-------------|
         |    ___      |
         \2*\/ 6  + 6*x/
------------------------
           12
6log⁡(6x−266x+26)12\frac{\sqrt{6} \log{\left(\frac{6 x - 2 \sqrt{6}}{6 x + 2 \sqrt{6}} \right)}}{12} 
sqrt(6)*log((6*x - 2*sqrt(6))/(2*sqrt(6) + 6*x))/12
Potencias [src] 
         /      ___      \
  ___    |- 2*\/ 6  + 6*x|
\/ 6 *log|---------------|
         |     ___       |
         \ 2*\/ 6  + 6*x /
--------------------------
            12
6log⁡(6x−266x+26)12\frac{\sqrt{6} \log{\left(\frac{6 x - 2 \sqrt{6}}{6 x + 2 \sqrt{6}} \right)}}{12} 
sqrt(6)*log((-2*sqrt(6) + 6*x)/(2*sqrt(6) + 6*x))/12
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