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Simplificación de expresiones/ Descomposición en fracciones simples/ log((2*y-2*sqrt(3))/(2*sqrt(3)+2*y))/(2*sqrt(3))

¿Cómo vas a descomponer esta log((2*y-2*sqrt(3))/(2*sqrt(3)+2*y))/(2*sqrt(3)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ___\
   |2*y - 2*\/ 3 |
log|-------------|
   |    ___      |
   \2*\/ 3  + 2*y/
------------------
         ___      
     2*\/ 3
$$\frac{\log{\left(\frac{2 y - 2 \sqrt{3}}{2 y + 2 \sqrt{3}} \right)}}{2 \sqrt{3}}$$ 
log((2*y - 2*sqrt(3))/(2*sqrt(3) + 2*y))/((2*sqrt(3)))
Simplificación general [src] 
         /      ___\
  ___    |y - \/ 3 |
\/ 3 *log|---------|
         |      ___|
         \y + \/ 3 /
--------------------
         6
$$\frac{\sqrt{3} \log{\left(\frac{y - \sqrt{3}}{y + \sqrt{3}} \right)}}{6}$$ 
sqrt(3)*log((y - sqrt(3))/(y + sqrt(3)))/6
Descomposición de una fracción [src] 
sqrt(3)*log(-2*sqrt(3)/(2*sqrt(3) + 2*y) + 2*y/(2*sqrt(3) + 2*y))/6
$$\frac{\sqrt{3} \log{\left(\frac{2 y}{2 y + 2 \sqrt{3}} - \frac{2 \sqrt{3}}{2 y + 2 \sqrt{3}} \right)}}{6}$$ 
         /         ___                   \
  ___    |     2*\/ 3            2*y     |
\/ 3 *log|- ------------- + -------------|
         |      ___             ___      |
         \  2*\/ 3  + 2*y   2*\/ 3  + 2*y/
------------------------------------------
                    6
Denominador común [src] 
         /                ___  \
  ___    |    y         \/ 3   |
\/ 3 *log|--------- - ---------|
         |      ___         ___|
         \y + \/ 3    y + \/ 3 /
--------------------------------
               6
$$\frac{\sqrt{3} \log{\left(\frac{y}{y + \sqrt{3}} - \frac{\sqrt{3}}{y + \sqrt{3}} \right)}}{6}$$ 
sqrt(3)*log(y/(y + sqrt(3)) - sqrt(3)/(y + sqrt(3)))/6
Denominador racional [src] 
         /     2         ___\
  ___    |3 + y  - 2*y*\/ 3 |
\/ 3 *log|------------------|
         |           2      |
         \     -3 + y       /
-----------------------------
              6
$$\frac{\sqrt{3} \log{\left(\frac{y^{2} - 2 \sqrt{3} y + 3}{y^{2} - 3} \right)}}{6}$$ 
sqrt(3)*log((3 + y^2 - 2*y*sqrt(3))/(-3 + y^2))/6
Parte trigonométrica [src] 
         /      ___      \
  ___    |- 2*\/ 3  + 2*y|
\/ 3 *log|---------------|
         |           ___ |
         \ 2*y + 2*\/ 3  /
--------------------------
            6
$$\frac{\sqrt{3} \log{\left(\frac{2 y - 2 \sqrt{3}}{2 y + 2 \sqrt{3}} \right)}}{6}$$ 
sqrt(3)*log((-2*sqrt(3) + 2*y)/(2*y + 2*sqrt(3)))/6
Unión de expresiones racionales [src] 
         /      ___\
  ___    |y - \/ 3 |
\/ 3 *log|---------|
         |      ___|
         \y + \/ 3 /
--------------------
         6
$$\frac{\sqrt{3} \log{\left(\frac{y - \sqrt{3}}{y + \sqrt{3}} \right)}}{6}$$ 
sqrt(3)*log((y - sqrt(3))/(y + sqrt(3)))/6
Potencias [src] 
         /      ___      \
  ___    |- 2*\/ 3  + 2*y|
\/ 3 *log|---------------|
         |           ___ |
         \ 2*y + 2*\/ 3  /
--------------------------
            6
$$\frac{\sqrt{3} \log{\left(\frac{2 y - 2 \sqrt{3}}{2 y + 2 \sqrt{3}} \right)}}{6}$$ 
sqrt(3)*log((-2*sqrt(3) + 2*y)/(2*y + 2*sqrt(3)))/6
Combinatoria [src] 
         /         ___                   \
  ___    |     2*\/ 3            2*y     |
\/ 3 *log|- ------------- + -------------|
         |            ___             ___|
         \  2*y + 2*\/ 3    2*y + 2*\/ 3 /
------------------------------------------
                    6
$$\frac{\sqrt{3} \log{\left(\frac{2 y}{2 y + 2 \sqrt{3}} - \frac{2 \sqrt{3}}{2 y + 2 \sqrt{3}} \right)}}{6}$$ 
sqrt(3)*log(-2*sqrt(3)/(2*y + 2*sqrt(3)) + 2*y/(2*y + 2*sqrt(3)))/6
Abrimos la expresión [src] 
         /          ___\
  ___    |2*y - 2*\/ 3 |
\/ 3 *log|-------------|
         |    ___      |
         \2*\/ 3  + 2*y/
------------------------
           6
$$\frac{\sqrt{3} \log{\left(\frac{2 y - 2 \sqrt{3}}{2 y + 2 \sqrt{3}} \right)}}{6}$$ 
sqrt(3)*log((2*y - 2*sqrt(3))/(2*sqrt(3) + 2*y))/6
Compilar la expresión [src] 
         /          ___\
  ___    |2*y - 2*\/ 3 |
\/ 3 *log|-------------|
         |    ___      |
         \2*\/ 3  + 2*y/
------------------------
           6
$$\frac{\sqrt{3} \log{\left(\frac{2 y - 2 \sqrt{3}}{2 y + 2 \sqrt{3}} \right)}}{6}$$ 
sqrt(3)*log((2*y - 2*sqrt(3))/(2*sqrt(3) + 2*y))/6
Respuesta numérica [src] 
0.288675134594813*log((2*y - 2*sqrt(3))/(2*sqrt(3) + 2*y))
0.288675134594813*log((2*y - 2*sqrt(3))/(2*sqrt(3) + 2*y))
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