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Simplificación de expresiones/ Descomposición en fracciones simples/ log((6*x-sqrt(13)-1)/(6*x+sqrt(13)-1))/sqrt(13)

¿Cómo vas a descomponer esta log((6*x-sqrt(13)-1)/(6*x+sqrt(13)-1))/sqrt(13) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /        ____    \
   |6*x - \/ 13  - 1|
log|----------------|
   |        ____    |
   \6*x + \/ 13  - 1/
---------------------
          ____       
        \/ 13
log⁡((6x−13)−1(6x+13)−1)13\frac{\log{\left(\frac{\left(6 x - \sqrt{13}\right) - 1}{\left(6 x + \sqrt{13}\right) - 1} \right)}}{\sqrt{13}} 
log((6*x - sqrt(13) - 1)/(6*x + sqrt(13) - 1))/sqrt(13)
Descomposición de una fracción [src] 
sqrt(13)*log(-1/(6*x + sqrt(13) - 1) - sqrt(13)/(6*x + sqrt(13) - 1) + 6*x/(6*x + sqrt(13) - 1))/13
13log⁡(6x(6x+13)−1−13(6x+13)−1−1(6x+13)−1)13\frac{\sqrt{13} \log{\left(\frac{6 x}{\left(6 x + \sqrt{13}\right) - 1} - \frac{\sqrt{13}}{\left(6 x + \sqrt{13}\right) - 1} - \frac{1}{\left(6 x + \sqrt{13}\right) - 1} \right)}}{13} 
          /                            ____                        \
  ____    |         1                \/ 13               6*x       |
\/ 13 *log|- ---------------- - ---------------- + ----------------|
          |          ____               ____               ____    |
          \  6*x + \/ 13  - 1   6*x + \/ 13  - 1   6*x + \/ 13  - 1/
--------------------------------------------------------------------
                                 13
Simplificación general [src] 
          /       ____      \
  ____    |-1 - \/ 13  + 6*x|
\/ 13 *log|-----------------|
          |       ____      |
          \-1 + \/ 13  + 6*x/
-----------------------------
              13
13log⁡(6x−13−16x−1+13)13\frac{\sqrt{13} \log{\left(\frac{6 x - \sqrt{13} - 1}{6 x - 1 + \sqrt{13}} \right)}}{13} 
sqrt(13)*log((-1 - sqrt(13) + 6*x)/(-1 + sqrt(13) + 6*x))/13
Respuesta numérica [src] 
0.277350098112615*log((6*x - sqrt(13) - 1)/(6*x + sqrt(13) - 1))
0.277350098112615*log((6*x - sqrt(13) - 1)/(6*x + sqrt(13) - 1))
Denominador racional [src] 
          / /      ____      \ \
  ____    |-\1 + \/ 13  - 6*x/ |
\/ 13 *log|--------------------|
          |        ____        |
          \ -1 + \/ 13  + 6*x  /
--------------------------------
               13
13log⁡(−−6x+1+136x−1+13)13\frac{\sqrt{13} \log{\left(- \frac{- 6 x + 1 + \sqrt{13}}{6 x - 1 + \sqrt{13}} \right)}}{13} 
sqrt(13)*log(-(1 + sqrt(13) - 6*x)/(-1 + sqrt(13) + 6*x))/13
Combinatoria [src] 
          /                              ____                         \
  ____    |          1                 \/ 13                6*x       |
\/ 13 *log|- ----------------- - ----------------- + -----------------|
          |         ____                ____                ____      |
          \  -1 + \/ 13  + 6*x   -1 + \/ 13  + 6*x   -1 + \/ 13  + 6*x/
-----------------------------------------------------------------------
                                   13
13log⁡(6x6x−1+13−136x−1+13−16x−1+13)13\frac{\sqrt{13} \log{\left(\frac{6 x}{6 x - 1 + \sqrt{13}} - \frac{\sqrt{13}}{6 x - 1 + \sqrt{13}} - \frac{1}{6 x - 1 + \sqrt{13}} \right)}}{13} 
sqrt(13)*log(-1/(-1 + sqrt(13) + 6*x) - sqrt(13)/(-1 + sqrt(13) + 6*x) + 6*x/(-1 + sqrt(13) + 6*x))/13
Denominador común [src] 
          /                              ____                         \
  ____    |          1                 \/ 13                6*x       |
\/ 13 *log|- ----------------- - ----------------- + -----------------|
          |         ____                ____                ____      |
          \  -1 + \/ 13  + 6*x   -1 + \/ 13  + 6*x   -1 + \/ 13  + 6*x/
-----------------------------------------------------------------------
                                   13
13log⁡(6x6x−1+13−136x−1+13−16x−1+13)13\frac{\sqrt{13} \log{\left(\frac{6 x}{6 x - 1 + \sqrt{13}} - \frac{\sqrt{13}}{6 x - 1 + \sqrt{13}} - \frac{1}{6 x - 1 + \sqrt{13}} \right)}}{13} 
sqrt(13)*log(-1/(-1 + sqrt(13) + 6*x) - sqrt(13)/(-1 + sqrt(13) + 6*x) + 6*x/(-1 + sqrt(13) + 6*x))/13
Unión de expresiones racionales [src] 
          /       ____      \
  ____    |-1 - \/ 13  + 6*x|
\/ 13 *log|-----------------|
          |       ____      |
          \-1 + \/ 13  + 6*x/
-----------------------------
              13
13log⁡(6x−13−16x−1+13)13\frac{\sqrt{13} \log{\left(\frac{6 x - \sqrt{13} - 1}{6 x - 1 + \sqrt{13}} \right)}}{13} 
sqrt(13)*log((-1 - sqrt(13) + 6*x)/(-1 + sqrt(13) + 6*x))/13
Potencias [src] 
          /       ____      \
  ____    |-1 - \/ 13  + 6*x|
\/ 13 *log|-----------------|
          |       ____      |
          \-1 + \/ 13  + 6*x/
-----------------------------
              13
13log⁡(6x−13−16x−1+13)13\frac{\sqrt{13} \log{\left(\frac{6 x - \sqrt{13} - 1}{6 x - 1 + \sqrt{13}} \right)}}{13} 
sqrt(13)*log((-1 - sqrt(13) + 6*x)/(-1 + sqrt(13) + 6*x))/13
Compilar la expresión [src] 
          /        ____    \
  ____    |6*x - \/ 13  - 1|
\/ 13 *log|----------------|
          |        ____    |
          \6*x + \/ 13  - 1/
----------------------------
             13
13log⁡((6x−13)−1(6x+13)−1)13\frac{\sqrt{13} \log{\left(\frac{\left(6 x - \sqrt{13}\right) - 1}{\left(6 x + \sqrt{13}\right) - 1} \right)}}{13} 
sqrt(13)*log((6*x - sqrt(13) - 1)/(6*x + sqrt(13) - 1))/13
Parte trigonométrica [src] 
          /       ____      \
  ____    |-1 - \/ 13  + 6*x|
\/ 13 *log|-----------------|
          |       ____      |
          \-1 + \/ 13  + 6*x/
-----------------------------
              13
13log⁡(6x−13−16x−1+13)13\frac{\sqrt{13} \log{\left(\frac{6 x - \sqrt{13} - 1}{6 x - 1 + \sqrt{13}} \right)}}{13} 
sqrt(13)*log((-1 - sqrt(13) + 6*x)/(-1 + sqrt(13) + 6*x))/13
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