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Simplificación de expresiones/ Descomposición en fracciones simples/ log((8*x-4*sqrt(3))/(4*sqrt(3)+8*x))/(4*sqrt(3))

¿Cómo vas a descomponer esta log((8*x-4*sqrt(3))/(4*sqrt(3)+8*x))/(4*sqrt(3)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ___\
   |8*x - 4*\/ 3 |
log|-------------|
   |    ___      |
   \4*\/ 3  + 8*x/
------------------
         ___      
     4*\/ 3
$$\frac{\log{\left(\frac{8 x - 4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{4 \sqrt{3}}$$ 
log((8*x - 4*sqrt(3))/(4*sqrt(3) + 8*x))/((4*sqrt(3)))
Simplificación general [src] 
         /    ___      \
  ___    |- \/ 3  + 2*x|
\/ 3 *log|-------------|
         |   ___       |
         \ \/ 3  + 2*x /
------------------------
           12
$$\frac{\sqrt{3} \log{\left(\frac{2 x - \sqrt{3}}{2 x + \sqrt{3}} \right)}}{12}$$ 
sqrt(3)*log((-sqrt(3) + 2*x)/(sqrt(3) + 2*x))/12
Descomposición de una fracción [src] 
sqrt(3)*log(-4*sqrt(3)/(4*sqrt(3) + 8*x) + 8*x/(4*sqrt(3) + 8*x))/12
$$\frac{\sqrt{3} \log{\left(\frac{8 x}{8 x + 4 \sqrt{3}} - \frac{4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$ 
         /         ___                   \
  ___    |     4*\/ 3            8*x     |
\/ 3 *log|- ------------- + -------------|
         |      ___             ___      |
         \  4*\/ 3  + 8*x   4*\/ 3  + 8*x/
------------------------------------------
                    12
Respuesta numérica [src] 
0.144337567297406*log((8*x - 4*sqrt(3))/(4*sqrt(3) + 8*x))
0.144337567297406*log((8*x - 4*sqrt(3))/(4*sqrt(3) + 8*x))
Parte trigonométrica [src] 
         /      ___      \
  ___    |- 4*\/ 3  + 8*x|
\/ 3 *log|---------------|
         |     ___       |
         \ 4*\/ 3  + 8*x /
--------------------------
            12
$$\frac{\sqrt{3} \log{\left(\frac{8 x - 4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$ 
sqrt(3)*log((-4*sqrt(3) + 8*x)/(4*sqrt(3) + 8*x))/12
Denominador común [src] 
         /       ___                 \
  ___    |     \/ 3           2*x    |
\/ 3 *log|- ----------- + -----------|
         |    ___           ___      |
         \  \/ 3  + 2*x   \/ 3  + 2*x/
--------------------------------------
                  12
$$\frac{\sqrt{3} \log{\left(\frac{2 x}{2 x + \sqrt{3}} - \frac{\sqrt{3}}{2 x + \sqrt{3}} \right)}}{12}$$ 
sqrt(3)*log(-sqrt(3)/(sqrt(3) + 2*x) + 2*x/(sqrt(3) + 2*x))/12
Combinatoria [src] 
         /         ___                   \
  ___    |     4*\/ 3            8*x     |
\/ 3 *log|- ------------- + -------------|
         |      ___             ___      |
         \  4*\/ 3  + 8*x   4*\/ 3  + 8*x/
------------------------------------------
                    12
$$\frac{\sqrt{3} \log{\left(\frac{8 x}{8 x + 4 \sqrt{3}} - \frac{4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$ 
sqrt(3)*log(-4*sqrt(3)/(4*sqrt(3) + 8*x) + 8*x/(4*sqrt(3) + 8*x))/12
Denominador racional [src] 
         /       2         ___\
  ___    |3 + 4*x  - 4*x*\/ 3 |
\/ 3 *log|--------------------|
         |             2      |
         \     -3 + 4*x       /
-------------------------------
               12
$$\frac{\sqrt{3} \log{\left(\frac{4 x^{2} - 4 \sqrt{3} x + 3}{4 x^{2} - 3} \right)}}{12}$$ 
sqrt(3)*log((3 + 4*x^2 - 4*x*sqrt(3))/(-3 + 4*x^2))/12
Unión de expresiones racionales [src] 
         /    ___      \
  ___    |- \/ 3  + 2*x|
\/ 3 *log|-------------|
         |   ___       |
         \ \/ 3  + 2*x /
------------------------
           12
$$\frac{\sqrt{3} \log{\left(\frac{2 x - \sqrt{3}}{2 x + \sqrt{3}} \right)}}{12}$$ 
sqrt(3)*log((-sqrt(3) + 2*x)/(sqrt(3) + 2*x))/12
Potencias [src] 
         /      ___      \
  ___    |- 4*\/ 3  + 8*x|
\/ 3 *log|---------------|
         |     ___       |
         \ 4*\/ 3  + 8*x /
--------------------------
            12
$$\frac{\sqrt{3} \log{\left(\frac{8 x - 4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$ 
sqrt(3)*log((-4*sqrt(3) + 8*x)/(4*sqrt(3) + 8*x))/12
Abrimos la expresión [src] 
         /          ___\
  ___    |8*x - 4*\/ 3 |
\/ 3 *log|-------------|
         |    ___      |
         \4*\/ 3  + 8*x/
------------------------
           12
$$\frac{\sqrt{3} \log{\left(\frac{8 x - 4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$ 
sqrt(3)*log((8*x - 4*sqrt(3))/(4*sqrt(3) + 8*x))/12
Compilar la expresión [src] 
         /          ___\
  ___    |8*x - 4*\/ 3 |
\/ 3 *log|-------------|
         |    ___      |
         \4*\/ 3  + 8*x/
------------------------
           12
$$\frac{\sqrt{3} \log{\left(\frac{8 x - 4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$ 
sqrt(3)*log((8*x - 4*sqrt(3))/(4*sqrt(3) + 8*x))/12
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