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Simplificación de expresiones/ Descomposición en fracciones simples/ log(2*x^2+4*x-1)/4-log((4*x-2*sqrt(6)+4)/(4+2*sqrt(6)+4*x))/(2*sqrt(6))

¿Cómo vas a descomponer esta log(2*x^2+4*x-1)/4-log((4*x-2*sqrt(6)+4)/(4+2*sqrt(6)+4*x))/(2*sqrt(6)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                         /          ___    \
                         |4*x - 2*\/ 6  + 4|
                      log|-----------------|
   /   2          \      |        ___      |
log\2*x  + 4*x - 1/      \4 + 2*\/ 6  + 4*x/
------------------- - ----------------------
         4                       ___        
                             2*\/ 6
−log⁡((4x−26)+44x+(4+26))26+log⁡((2x2+4x)−1)4- \frac{\log{\left(\frac{\left(4 x - 2 \sqrt{6}\right) + 4}{4 x + \left(4 + 2 \sqrt{6}\right)} \right)}}{2 \sqrt{6}} + \frac{\log{\left(\left(2 x^{2} + 4 x\right) - 1 \right)}}{4} 
log(2*x^2 + 4*x - 1)/4 - log((4*x - 2*sqrt(6) + 4)/(4 + 2*sqrt(6) + 4*x))/(2*sqrt(6))
Simplificación general [src] 
                                /      ___      \
                         ___    |2 - \/ 6  + 2*x|
                       \/ 6 *log|---------------|
   /        2      \            |      ___      |
log\-1 + 2*x  + 4*x/            \2 + \/ 6  + 2*x/
-------------------- - --------------------------
         4                         12
−6log⁡(2x−6+22x+2+6)12+log⁡(2x2+4x−1)4- \frac{\sqrt{6} \log{\left(\frac{2 x - \sqrt{6} + 2}{2 x + 2 + \sqrt{6}} \right)}}{12} + \frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4} 
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log((2 - sqrt(6) + 2*x)/(2 + sqrt(6) + 2*x))/12
Respuesta numérica [src] 
0.25*log(2*x^2 + 4*x - 1) - 0.204124145231932*log((4*x - 2*sqrt(6) + 4)/(4 + 2*sqrt(6) + 4*x))
0.25*log(2*x^2 + 4*x - 1) - 0.204124145231932*log((4*x - 2*sqrt(6) + 4)/(4 + 2*sqrt(6) + 4*x))
Parte trigonométrica [src] 
                                /        ___      \
                         ___    |4 - 2*\/ 6  + 4*x|
                       \/ 6 *log|-----------------|
   /        2      \            |        ___      |
log\-1 + 2*x  + 4*x/            \4 + 2*\/ 6  + 4*x/
-------------------- - ----------------------------
         4                          12
−6log⁡(4x−26+44x+4+26)12+log⁡(2x2+4x−1)4- \frac{\sqrt{6} \log{\left(\frac{4 x - 2 \sqrt{6} + 4}{4 x + 4 + 2 \sqrt{6}} \right)}}{12} + \frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4} 
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log((4 - 2*sqrt(6) + 4*x)/(4 + 2*sqrt(6) + 4*x))/12
Combinatoria [src] 
                                /                             ___                         \
                         ___    |        4                2*\/ 6                4*x       |
                       \/ 6 *log|----------------- - ----------------- + -----------------|
   /        2      \            |        ___                 ___                 ___      |
log\-1 + 2*x  + 4*x/            \4 + 2*\/ 6  + 4*x   4 + 2*\/ 6  + 4*x   4 + 2*\/ 6  + 4*x/
-------------------- - --------------------------------------------------------------------
         4                                              12
log⁡(2x2+4x−1)4−6log⁡(4x4x+4+26−264x+4+26+44x+4+26)12\frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4} - \frac{\sqrt{6} \log{\left(\frac{4 x}{4 x + 4 + 2 \sqrt{6}} - \frac{2 \sqrt{6}}{4 x + 4 + 2 \sqrt{6}} + \frac{4}{4 x + 4 + 2 \sqrt{6}} \right)}}{12} 
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log(4/(4 + 2*sqrt(6) + 4*x) - 2*sqrt(6)/(4 + 2*sqrt(6) + 4*x) + 4*x/(4 + 2*sqrt(6) + 4*x))/12
Potencias [src] 
                                /        ___      \
                         ___    |4 - 2*\/ 6  + 4*x|
                       \/ 6 *log|-----------------|
   /        2      \            |        ___      |
log\-1 + 2*x  + 4*x/            \4 + 2*\/ 6  + 4*x/
-------------------- - ----------------------------
         4                          12
−6log⁡(4x−26+44x+4+26)12+log⁡(2x2+4x−1)4- \frac{\sqrt{6} \log{\left(\frac{4 x - 2 \sqrt{6} + 4}{4 x + 4 + 2 \sqrt{6}} \right)}}{12} + \frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4} 
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log((4 - 2*sqrt(6) + 4*x)/(4 + 2*sqrt(6) + 4*x))/12
Denominador racional [src] 
                                  /                             ___                         \
     /        2      \     ___    |        4                2*\/ 6                4*x       |
3*log\-1 + 2*x  + 4*x/ - \/ 6 *log|----------------- - ----------------- + -----------------|
                                  |        ___                 ___                 ___      |
                                  \4 + 2*\/ 6  + 4*x   4 + 2*\/ 6  + 4*x   4 + 2*\/ 6  + 4*x/
---------------------------------------------------------------------------------------------
                                              12
3log⁡(2x2+4x−1)−6log⁡(4x4x+(4+26)−264x+(4+26)+44x+(4+26))12\frac{3 \log{\left(2 x^{2} + 4 x - 1 \right)} - \sqrt{6} \log{\left(\frac{4 x}{4 x + \left(4 + 2 \sqrt{6}\right)} - \frac{2 \sqrt{6}}{4 x + \left(4 + 2 \sqrt{6}\right)} + \frac{4}{4 x + \left(4 + 2 \sqrt{6}\right)} \right)}}{12} 
(3*log(-1 + 2*x^2 + 4*x) - sqrt(6)*log(4/(4 + 2*sqrt(6) + 4*x) - 2*sqrt(6)/(4 + 2*sqrt(6) + 4*x) + 4*x/(4 + 2*sqrt(6) + 4*x)))/12
Denominador común [src] 
                                /                         ___                       \
                         ___    |       2               \/ 6               2*x      |
                       \/ 6 *log|--------------- - --------------- + ---------------|
   /        2      \            |      ___               ___               ___      |
log\-1 + 2*x  + 4*x/            \2 + \/ 6  + 2*x   2 + \/ 6  + 2*x   2 + \/ 6  + 2*x/
-------------------- - --------------------------------------------------------------
         4                                           12
log⁡(2x2+4x−1)4−6log⁡(2x2x+2+6−62x+2+6+22x+2+6)12\frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4} - \frac{\sqrt{6} \log{\left(\frac{2 x}{2 x + 2 + \sqrt{6}} - \frac{\sqrt{6}}{2 x + 2 + \sqrt{6}} + \frac{2}{2 x + 2 + \sqrt{6}} \right)}}{12} 
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log(2/(2 + sqrt(6) + 2*x) - sqrt(6)/(2 + sqrt(6) + 2*x) + 2*x/(2 + sqrt(6) + 2*x))/12
Unión de expresiones racionales [src] 
                                   /      ___      \
                            ___    |2 - \/ 6  + 2*x|
3*log(-1 + 2*x*(2 + x)) - \/ 6 *log|---------------|
                                   |      ___      |
                                   \2 + \/ 6  + 2*x/
----------------------------------------------------
                         12
−6log⁡(2x−6+22x+2+6)+3log⁡(2x(x+2)−1)12\frac{- \sqrt{6} \log{\left(\frac{2 x - \sqrt{6} + 2}{2 x + 2 + \sqrt{6}} \right)} + 3 \log{\left(2 x \left(x + 2\right) - 1 \right)}}{12} 
(3*log(-1 + 2*x*(2 + x)) - sqrt(6)*log((2 - sqrt(6) + 2*x)/(2 + sqrt(6) + 2*x)))/12
Compilar la expresión [src] 
                               /          ___    \
                        ___    |4*x - 2*\/ 6  + 4|
                      \/ 6 *log|-----------------|
   /   2          \            |        ___      |
log\2*x  + 4*x - 1/            \4 + 2*\/ 6  + 4*x/
------------------- - ----------------------------
         4                         12
−6log⁡((4x−26)+44x+(4+26))12+log⁡((2x2+4x)−1)4- \frac{\sqrt{6} \log{\left(\frac{\left(4 x - 2 \sqrt{6}\right) + 4}{4 x + \left(4 + 2 \sqrt{6}\right)} \right)}}{12} + \frac{\log{\left(\left(2 x^{2} + 4 x\right) - 1 \right)}}{4} 
log(2*x^2 + 4*x - 1)/4 - sqrt(6)*log((4*x - 2*sqrt(6) + 4)/(4 + 2*sqrt(6) + 4*x))/12
Abrimos la expresión [src] 
                               /          ___    \
                        ___    |4*x - 2*\/ 6  + 4|
                      \/ 6 *log|-----------------|
   /   2          \            |        ___      |
log\2*x  + 4*x - 1/            \4 + 2*\/ 6  + 4*x/
------------------- - ----------------------------
         4                         12
−6log⁡((4x−26)+44x+(4+26))12+log⁡((2x2+4x)−1)4- \frac{\sqrt{6} \log{\left(\frac{\left(4 x - 2 \sqrt{6}\right) + 4}{4 x + \left(4 + 2 \sqrt{6}\right)} \right)}}{12} + \frac{\log{\left(\left(2 x^{2} + 4 x\right) - 1 \right)}}{4} 
log(2*x^2 + 4*x - 1)/4 - sqrt(6)*log((4*x - 2*sqrt(6) + 4)/(4 + 2*sqrt(6) + 4*x))/12
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