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Simplificación de expresiones/ Descomposición en fracciones simples/ log((6*x-4*sqrt(3))/(4*sqrt(3)+6*x))/(4*sqrt(3))

¿Cómo vas a descomponer esta log((6*x-4*sqrt(3))/(4*sqrt(3)+6*x))/(4*sqrt(3)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ___\
   |6*x - 4*\/ 3 |
log|-------------|
   |    ___      |
   \4*\/ 3  + 6*x/
------------------
         ___      
     4*\/ 3
log⁡(6x−436x+43)43\frac{\log{\left(\frac{6 x - 4 \sqrt{3}}{6 x + 4 \sqrt{3}} \right)}}{4 \sqrt{3}} 
log((6*x - 4*sqrt(3))/(4*sqrt(3) + 6*x))/((4*sqrt(3)))
Simplificación general [src] 
         /      ___      \
  ___    |- 2*\/ 3  + 3*x|
\/ 3 *log|---------------|
         |     ___       |
         \ 2*\/ 3  + 3*x /
--------------------------
            12
3log⁡(3x−233x+23)12\frac{\sqrt{3} \log{\left(\frac{3 x - 2 \sqrt{3}}{3 x + 2 \sqrt{3}} \right)}}{12} 
sqrt(3)*log((-2*sqrt(3) + 3*x)/(2*sqrt(3) + 3*x))/12
Descomposición de una fracción [src] 
sqrt(3)*log(-4*sqrt(3)/(4*sqrt(3) + 6*x) + 6*x/(4*sqrt(3) + 6*x))/12
3log⁡(6x6x+43−436x+43)12\frac{\sqrt{3} \log{\left(\frac{6 x}{6 x + 4 \sqrt{3}} - \frac{4 \sqrt{3}}{6 x + 4 \sqrt{3}} \right)}}{12} 
         /         ___                   \
  ___    |     4*\/ 3            6*x     |
\/ 3 *log|- ------------- + -------------|
         |      ___             ___      |
         \  4*\/ 3  + 6*x   4*\/ 3  + 6*x/
------------------------------------------
                    12
Respuesta numérica [src] 
0.144337567297406*log((6*x - 4*sqrt(3))/(4*sqrt(3) + 6*x))
0.144337567297406*log((6*x - 4*sqrt(3))/(4*sqrt(3) + 6*x))
Parte trigonométrica [src] 
         /      ___      \
  ___    |- 4*\/ 3  + 6*x|
\/ 3 *log|---------------|
         |     ___       |
         \ 4*\/ 3  + 6*x /
--------------------------
            12
3log⁡(6x−436x+43)12\frac{\sqrt{3} \log{\left(\frac{6 x - 4 \sqrt{3}}{6 x + 4 \sqrt{3}} \right)}}{12} 
sqrt(3)*log((-4*sqrt(3) + 6*x)/(4*sqrt(3) + 6*x))/12
Denominador racional [src] 
         /       2         ___\
  ___    |4 + 3*x  - 4*x*\/ 3 |
\/ 3 *log|--------------------|
         |             2      |
         \     -4 + 3*x       /
-------------------------------
               12
3log⁡(3x2−43x+43x2−4)12\frac{\sqrt{3} \log{\left(\frac{3 x^{2} - 4 \sqrt{3} x + 4}{3 x^{2} - 4} \right)}}{12} 
sqrt(3)*log((4 + 3*x^2 - 4*x*sqrt(3))/(-4 + 3*x^2))/12
Denominador común [src] 
         /         ___                   \
  ___    |     2*\/ 3            3*x     |
\/ 3 *log|- ------------- + -------------|
         |      ___             ___      |
         \  2*\/ 3  + 3*x   2*\/ 3  + 3*x/
------------------------------------------
                    12
3log⁡(3x3x+23−233x+23)12\frac{\sqrt{3} \log{\left(\frac{3 x}{3 x + 2 \sqrt{3}} - \frac{2 \sqrt{3}}{3 x + 2 \sqrt{3}} \right)}}{12} 
sqrt(3)*log(-2*sqrt(3)/(2*sqrt(3) + 3*x) + 3*x/(2*sqrt(3) + 3*x))/12
Potencias [src] 
         /      ___      \
  ___    |- 4*\/ 3  + 6*x|
\/ 3 *log|---------------|
         |     ___       |
         \ 4*\/ 3  + 6*x /
--------------------------
            12
3log⁡(6x−436x+43)12\frac{\sqrt{3} \log{\left(\frac{6 x - 4 \sqrt{3}}{6 x + 4 \sqrt{3}} \right)}}{12} 
sqrt(3)*log((-4*sqrt(3) + 6*x)/(4*sqrt(3) + 6*x))/12
Combinatoria [src] 
         /         ___                   \
  ___    |     4*\/ 3            6*x     |
\/ 3 *log|- ------------- + -------------|
         |      ___             ___      |
         \  4*\/ 3  + 6*x   4*\/ 3  + 6*x/
------------------------------------------
                    12
3log⁡(6x6x+43−436x+43)12\frac{\sqrt{3} \log{\left(\frac{6 x}{6 x + 4 \sqrt{3}} - \frac{4 \sqrt{3}}{6 x + 4 \sqrt{3}} \right)}}{12} 
sqrt(3)*log(-4*sqrt(3)/(4*sqrt(3) + 6*x) + 6*x/(4*sqrt(3) + 6*x))/12
Unión de expresiones racionales [src] 
         /      ___      \
  ___    |- 2*\/ 3  + 3*x|
\/ 3 *log|---------------|
         |     ___       |
         \ 2*\/ 3  + 3*x /
--------------------------
            12
3log⁡(3x−233x+23)12\frac{\sqrt{3} \log{\left(\frac{3 x - 2 \sqrt{3}}{3 x + 2 \sqrt{3}} \right)}}{12} 
sqrt(3)*log((-2*sqrt(3) + 3*x)/(2*sqrt(3) + 3*x))/12
Abrimos la expresión [src] 
         /          ___\
  ___    |6*x - 4*\/ 3 |
\/ 3 *log|-------------|
         |    ___      |
         \4*\/ 3  + 6*x/
------------------------
           12
3log⁡(6x−436x+43)12\frac{\sqrt{3} \log{\left(\frac{6 x - 4 \sqrt{3}}{6 x + 4 \sqrt{3}} \right)}}{12} 
sqrt(3)*log((6*x - 4*sqrt(3))/(4*sqrt(3) + 6*x))/12
Compilar la expresión [src] 
         /          ___\
  ___    |6*x - 4*\/ 3 |
\/ 3 *log|-------------|
         |    ___      |
         \4*\/ 3  + 6*x/
------------------------
           12
3log⁡(6x−436x+43)12\frac{\sqrt{3} \log{\left(\frac{6 x - 4 \sqrt{3}}{6 x + 4 \sqrt{3}} \right)}}{12} 
sqrt(3)*log((6*x - 4*sqrt(3))/(4*sqrt(3) + 6*x))/12
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