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Simplificación de expresiones/ Descomposición en fracciones simples/ log((2*x-3*sqrt(5)+7)/(2*x+3*sqrt(5)+7))/(3*sqrt(5))

¿Cómo vas a descomponer esta log((2*x-3*sqrt(5)+7)/(2*x+3*sqrt(5)+7))/(3*sqrt(5)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ___    \
   |2*x - 3*\/ 5  + 7|
log|-----------------|
   |          ___    |
   \2*x + 3*\/ 5  + 7/
----------------------
           ___        
       3*\/ 5
$$\frac{\log{\left(\frac{\left(2 x - 3 \sqrt{5}\right) + 7}{\left(2 x + 3 \sqrt{5}\right) + 7} \right)}}{3 \sqrt{5}}$$ 
log((2*x - 3*sqrt(5) + 7)/(2*x + 3*sqrt(5) + 7))/((3*sqrt(5)))
Simplificación general [src] 
         /        ___      \
  ___    |7 - 3*\/ 5  + 2*x|
\/ 5 *log|-----------------|
         |              ___|
         \7 + 2*x + 3*\/ 5 /
----------------------------
             15
$$\frac{\sqrt{5} \log{\left(\frac{2 x - 3 \sqrt{5} + 7}{2 x + 3 \sqrt{5} + 7} \right)}}{15}$$ 
sqrt(5)*log((7 - 3*sqrt(5) + 2*x)/(7 + 2*x + 3*sqrt(5)))/15
Descomposición de una fracción [src] 
sqrt(5)*log(7/(2*x + 3*sqrt(5) + 7) - 3*sqrt(5)/(2*x + 3*sqrt(5) + 7) + 2*x/(2*x + 3*sqrt(5) + 7))/15
$$\frac{\sqrt{5} \log{\left(\frac{2 x}{\left(2 x + 3 \sqrt{5}\right) + 7} - \frac{3 \sqrt{5}}{\left(2 x + 3 \sqrt{5}\right) + 7} + \frac{7}{\left(2 x + 3 \sqrt{5}\right) + 7} \right)}}{15}$$ 
         /                             ___                         \
  ___    |        7                3*\/ 5                2*x       |
\/ 5 *log|----------------- - ----------------- + -----------------|
         |          ___                 ___                 ___    |
         \2*x + 3*\/ 5  + 7   2*x + 3*\/ 5  + 7   2*x + 3*\/ 5  + 7/
--------------------------------------------------------------------
                                 15
Respuesta numérica [src] 
0.149071198499986*log((2*x - 3*sqrt(5) + 7)/(2*x + 3*sqrt(5) + 7))
0.149071198499986*log((2*x - 3*sqrt(5) + 7)/(2*x + 3*sqrt(5) + 7))
Unión de expresiones racionales [src] 
         /        ___      \
  ___    |7 - 3*\/ 5  + 2*x|
\/ 5 *log|-----------------|
         |              ___|
         \7 + 2*x + 3*\/ 5 /
----------------------------
             15
$$\frac{\sqrt{5} \log{\left(\frac{2 x - 3 \sqrt{5} + 7}{2 x + 3 \sqrt{5} + 7} \right)}}{15}$$ 
sqrt(5)*log((7 - 3*sqrt(5) + 2*x)/(7 + 2*x + 3*sqrt(5)))/15
Denominador racional [src] 
         /        ___      \
  ___    |7 - 3*\/ 5  + 2*x|
\/ 5 *log|-----------------|
         |          ___    |
         \2*x + 3*\/ 5  + 7/
----------------------------
             15
$$\frac{\sqrt{5} \log{\left(\frac{2 x - 3 \sqrt{5} + 7}{\left(2 x + 3 \sqrt{5}\right) + 7} \right)}}{15}$$ 
sqrt(5)*log((7 - 3*sqrt(5) + 2*x)/(2*x + 3*sqrt(5) + 7))/15
Potencias [src] 
         /        ___      \
  ___    |7 - 3*\/ 5  + 2*x|
\/ 5 *log|-----------------|
         |              ___|
         \7 + 2*x + 3*\/ 5 /
----------------------------
             15
$$\frac{\sqrt{5} \log{\left(\frac{2 x - 3 \sqrt{5} + 7}{2 x + 3 \sqrt{5} + 7} \right)}}{15}$$ 
sqrt(5)*log((7 - 3*sqrt(5) + 2*x)/(7 + 2*x + 3*sqrt(5)))/15
Parte trigonométrica [src] 
         /        ___      \
  ___    |7 - 3*\/ 5  + 2*x|
\/ 5 *log|-----------------|
         |              ___|
         \7 + 2*x + 3*\/ 5 /
----------------------------
             15
$$\frac{\sqrt{5} \log{\left(\frac{2 x - 3 \sqrt{5} + 7}{2 x + 3 \sqrt{5} + 7} \right)}}{15}$$ 
sqrt(5)*log((7 - 3*sqrt(5) + 2*x)/(7 + 2*x + 3*sqrt(5)))/15
Combinatoria [src] 
         /                             ___                         \
  ___    |        7                3*\/ 5                2*x       |
\/ 5 *log|----------------- - ----------------- + -----------------|
         |              ___                 ___                 ___|
         \7 + 2*x + 3*\/ 5    7 + 2*x + 3*\/ 5    7 + 2*x + 3*\/ 5 /
--------------------------------------------------------------------
                                 15
$$\frac{\sqrt{5} \log{\left(\frac{2 x}{2 x + 3 \sqrt{5} + 7} - \frac{3 \sqrt{5}}{2 x + 3 \sqrt{5} + 7} + \frac{7}{2 x + 3 \sqrt{5} + 7} \right)}}{15}$$ 
sqrt(5)*log(7/(7 + 2*x + 3*sqrt(5)) - 3*sqrt(5)/(7 + 2*x + 3*sqrt(5)) + 2*x/(7 + 2*x + 3*sqrt(5)))/15
Denominador común [src] 
         /                             ___                         \
  ___    |        7                3*\/ 5                2*x       |
\/ 5 *log|----------------- - ----------------- + -----------------|
         |              ___                 ___                 ___|
         \7 + 2*x + 3*\/ 5    7 + 2*x + 3*\/ 5    7 + 2*x + 3*\/ 5 /
--------------------------------------------------------------------
                                 15
$$\frac{\sqrt{5} \log{\left(\frac{2 x}{2 x + 3 \sqrt{5} + 7} - \frac{3 \sqrt{5}}{2 x + 3 \sqrt{5} + 7} + \frac{7}{2 x + 3 \sqrt{5} + 7} \right)}}{15}$$ 
sqrt(5)*log(7/(7 + 2*x + 3*sqrt(5)) - 3*sqrt(5)/(7 + 2*x + 3*sqrt(5)) + 2*x/(7 + 2*x + 3*sqrt(5)))/15
Compilar la expresión [src] 
         /          ___    \
  ___    |2*x - 3*\/ 5  + 7|
\/ 5 *log|-----------------|
         |          ___    |
         \2*x + 3*\/ 5  + 7/
----------------------------
             15
$$\frac{\sqrt{5} \log{\left(\frac{\left(2 x - 3 \sqrt{5}\right) + 7}{\left(2 x + 3 \sqrt{5}\right) + 7} \right)}}{15}$$ 
sqrt(5)*log((2*x - 3*sqrt(5) + 7)/(2*x + 3*sqrt(5) + 7))/15
Abrimos la expresión [src] 
         /          ___    \
  ___    |2*x - 3*\/ 5  + 7|
\/ 5 *log|-----------------|
         |          ___    |
         \2*x + 3*\/ 5  + 7/
----------------------------
             15
$$\frac{\sqrt{5} \log{\left(\frac{\left(2 x - 3 \sqrt{5}\right) + 7}{\left(2 x + 3 \sqrt{5}\right) + 7} \right)}}{15}$$ 
sqrt(5)*log((2*x - 3*sqrt(5) + 7)/(2*x + 3*sqrt(5) + 7))/15
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