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Simplificación de expresiones/ Descomposición en fracciones simples/ log((6*x-2*sqrt(39)+12)/(12+2*sqrt(39)+6*x))/(2*sqrt(39))

¿Cómo vas a descomponer esta log((6*x-2*sqrt(39)+12)/(12+2*sqrt(39)+6*x))/(2*sqrt(39)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ____     \
   |6*x - 2*\/ 39  + 12|
log|-------------------|
   |         ____      |
   \12 + 2*\/ 39  + 6*x/
------------------------
            ____        
        2*\/ 39
log⁡((6x−239)+126x+(12+239))239\frac{\log{\left(\frac{\left(6 x - 2 \sqrt{39}\right) + 12}{6 x + \left(12 + 2 \sqrt{39}\right)} \right)}}{2 \sqrt{39}} 
log((6*x - 2*sqrt(39) + 12)/(12 + 2*sqrt(39) + 6*x))/((2*sqrt(39)))
Simplificación general [src] 
          /      ____      \
  ____    |6 - \/ 39  + 3*x|
\/ 39 *log|----------------|
          |      ____      |
          \6 + \/ 39  + 3*x/
----------------------------
             78
39log⁡(3x−39+63x+6+39)78\frac{\sqrt{39} \log{\left(\frac{3 x - \sqrt{39} + 6}{3 x + 6 + \sqrt{39}} \right)}}{78} 
sqrt(39)*log((6 - sqrt(39) + 3*x)/(6 + sqrt(39) + 3*x))/78
Descomposición de una fracción [src] 
sqrt(39)*log(12/(12 + 2*sqrt(39) + 6*x) - 2*sqrt(39)/(12 + 2*sqrt(39) + 6*x) + 6*x/(12 + 2*sqrt(39) + 6*x))/78
39log⁡(6x6x+(12+239)−2396x+(12+239)+126x+(12+239))78\frac{\sqrt{39} \log{\left(\frac{6 x}{6 x + \left(12 + 2 \sqrt{39}\right)} - \frac{2 \sqrt{39}}{6 x + \left(12 + 2 \sqrt{39}\right)} + \frac{12}{6 x + \left(12 + 2 \sqrt{39}\right)} \right)}}{78} 
          /                                ____                           \
  ____    |         12                 2*\/ 39                 6*x        |
\/ 39 *log|------------------- - ------------------- + -------------------|
          |         ____                  ____                  ____      |
          \12 + 2*\/ 39  + 6*x   12 + 2*\/ 39  + 6*x   12 + 2*\/ 39  + 6*x/
---------------------------------------------------------------------------
                                     78
Respuesta numérica [src] 
0.0800640769025436*log((6*x - 2*sqrt(39) + 12)/(12 + 2*sqrt(39) + 6*x))
0.0800640769025436*log((6*x - 2*sqrt(39) + 12)/(12 + 2*sqrt(39) + 6*x))
Parte trigonométrica [src] 
          /         ____      \
  ____    |12 - 2*\/ 39  + 6*x|
\/ 39 *log|-------------------|
          |         ____      |
          \12 + 2*\/ 39  + 6*x/
-------------------------------
               78
39log⁡(6x−239+126x+12+239)78\frac{\sqrt{39} \log{\left(\frac{6 x - 2 \sqrt{39} + 12}{6 x + 12 + 2 \sqrt{39}} \right)}}{78} 
sqrt(39)*log((12 - 2*sqrt(39) + 6*x)/(12 + 2*sqrt(39) + 6*x))/78
Denominador común [src] 
          /                          ____                        \
  ____    |       6                \/ 39               3*x       |
\/ 39 *log|---------------- - ---------------- + ----------------|
          |      ____               ____               ____      |
          \6 + \/ 39  + 3*x   6 + \/ 39  + 3*x   6 + \/ 39  + 3*x/
------------------------------------------------------------------
                                78
39log⁡(3x3x+6+39−393x+6+39+63x+6+39)78\frac{\sqrt{39} \log{\left(\frac{3 x}{3 x + 6 + \sqrt{39}} - \frac{\sqrt{39}}{3 x + 6 + \sqrt{39}} + \frac{6}{3 x + 6 + \sqrt{39}} \right)}}{78} 
sqrt(39)*log(6/(6 + sqrt(39) + 3*x) - sqrt(39)/(6 + sqrt(39) + 3*x) + 3*x/(6 + sqrt(39) + 3*x))/78
Potencias [src] 
          /         ____      \
  ____    |12 - 2*\/ 39  + 6*x|
\/ 39 *log|-------------------|
          |         ____      |
          \12 + 2*\/ 39  + 6*x/
-------------------------------
               78
39log⁡(6x−239+126x+12+239)78\frac{\sqrt{39} \log{\left(\frac{6 x - 2 \sqrt{39} + 12}{6 x + 12 + 2 \sqrt{39}} \right)}}{78} 
sqrt(39)*log((12 - 2*sqrt(39) + 6*x)/(12 + 2*sqrt(39) + 6*x))/78
Denominador racional [src] 
          /  /      ____      \\
  ____    |2*\6 - \/ 39  + 3*x/|
\/ 39 *log|--------------------|
          |         ____       |
          \12 + 2*\/ 39  + 6*x /
--------------------------------
               78
39log⁡(2(3x−39+6)6x+(12+239))78\frac{\sqrt{39} \log{\left(\frac{2 \left(3 x - \sqrt{39} + 6\right)}{6 x + \left(12 + 2 \sqrt{39}\right)} \right)}}{78} 
sqrt(39)*log(2*(6 - sqrt(39) + 3*x)/(12 + 2*sqrt(39) + 6*x))/78
Unión de expresiones racionales [src] 
          /      ____      \
  ____    |6 - \/ 39  + 3*x|
\/ 39 *log|----------------|
          |      ____      |
          \6 + \/ 39  + 3*x/
----------------------------
             78
39log⁡(3x−39+63x+6+39)78\frac{\sqrt{39} \log{\left(\frac{3 x - \sqrt{39} + 6}{3 x + 6 + \sqrt{39}} \right)}}{78} 
sqrt(39)*log((6 - sqrt(39) + 3*x)/(6 + sqrt(39) + 3*x))/78
Combinatoria [src] 
          /                                ____                           \
  ____    |         12                 2*\/ 39                 6*x        |
\/ 39 *log|------------------- - ------------------- + -------------------|
          |         ____                  ____                  ____      |
          \12 + 2*\/ 39  + 6*x   12 + 2*\/ 39  + 6*x   12 + 2*\/ 39  + 6*x/
---------------------------------------------------------------------------
                                     78
39log⁡(6x6x+12+239−2396x+12+239+126x+12+239)78\frac{\sqrt{39} \log{\left(\frac{6 x}{6 x + 12 + 2 \sqrt{39}} - \frac{2 \sqrt{39}}{6 x + 12 + 2 \sqrt{39}} + \frac{12}{6 x + 12 + 2 \sqrt{39}} \right)}}{78} 
sqrt(39)*log(12/(12 + 2*sqrt(39) + 6*x) - 2*sqrt(39)/(12 + 2*sqrt(39) + 6*x) + 6*x/(12 + 2*sqrt(39) + 6*x))/78
Compilar la expresión [src] 
          /          ____     \
  ____    |6*x - 2*\/ 39  + 12|
\/ 39 *log|-------------------|
          |         ____      |
          \12 + 2*\/ 39  + 6*x/
-------------------------------
               78
39log⁡((6x−239)+126x+(12+239))78\frac{\sqrt{39} \log{\left(\frac{\left(6 x - 2 \sqrt{39}\right) + 12}{6 x + \left(12 + 2 \sqrt{39}\right)} \right)}}{78} 
sqrt(39)*log((6*x - 2*sqrt(39) + 12)/(12 + 2*sqrt(39) + 6*x))/78
Abrimos la expresión [src] 
          /          ____     \
  ____    |6*x - 2*\/ 39  + 12|
\/ 39 *log|-------------------|
          |         ____      |
          \12 + 2*\/ 39  + 6*x/
-------------------------------
               78
39log⁡((6x−239)+126x+(12+239))78\frac{\sqrt{39} \log{\left(\frac{\left(6 x - 2 \sqrt{39}\right) + 12}{6 x + \left(12 + 2 \sqrt{39}\right)} \right)}}{78} 
sqrt(39)*log((6*x - 2*sqrt(39) + 12)/(12 + 2*sqrt(39) + 6*x))/78
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