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Simplificación de expresiones/ Descomposición en fracciones simples/ log((2*x-2*sqrt(7)+4)/(4+2*sqrt(7)+2*x))/(2*sqrt(7))

¿Cómo vas a descomponer esta log((2*x-2*sqrt(7)+4)/(4+2*sqrt(7)+2*x))/(2*sqrt(7)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ___    \
   |2*x - 2*\/ 7  + 4|
log|-----------------|
   |        ___      |
   \4 + 2*\/ 7  + 2*x/
----------------------
           ___        
       2*\/ 7
log⁡((2x−27)+42x+(4+27))27\frac{\log{\left(\frac{\left(2 x - 2 \sqrt{7}\right) + 4}{2 x + \left(4 + 2 \sqrt{7}\right)} \right)}}{2 \sqrt{7}} 
log((2*x - 2*sqrt(7) + 4)/(4 + 2*sqrt(7) + 2*x))/((2*sqrt(7)))
Descomposición de una fracción [src] 
sqrt(7)*log(4/(4 + 2*sqrt(7) + 2*x) - 2*sqrt(7)/(4 + 2*sqrt(7) + 2*x) + 2*x/(4 + 2*sqrt(7) + 2*x))/14
7log⁡(2x2x+(4+27)−272x+(4+27)+42x+(4+27))14\frac{\sqrt{7} \log{\left(\frac{2 x}{2 x + \left(4 + 2 \sqrt{7}\right)} - \frac{2 \sqrt{7}}{2 x + \left(4 + 2 \sqrt{7}\right)} + \frac{4}{2 x + \left(4 + 2 \sqrt{7}\right)} \right)}}{14} 
         /                             ___                         \
  ___    |        4                2*\/ 7                2*x       |
\/ 7 *log|----------------- - ----------------- + -----------------|
         |        ___                 ___                 ___      |
         \4 + 2*\/ 7  + 2*x   4 + 2*\/ 7  + 2*x   4 + 2*\/ 7  + 2*x/
--------------------------------------------------------------------
                                 14
Simplificación general [src] 
         /          ___\
  ___    |2 + x - \/ 7 |
\/ 7 *log|-------------|
         |          ___|
         \2 + x + \/ 7 /
------------------------
           14
7log⁡(x−7+2x+2+7)14\frac{\sqrt{7} \log{\left(\frac{x - \sqrt{7} + 2}{x + 2 + \sqrt{7}} \right)}}{14} 
sqrt(7)*log((2 + x - sqrt(7))/(2 + x + sqrt(7)))/14
Respuesta numérica [src] 
0.188982236504614*log((2*x - 2*sqrt(7) + 4)/(4 + 2*sqrt(7) + 2*x))
0.188982236504614*log((2*x - 2*sqrt(7) + 4)/(4 + 2*sqrt(7) + 2*x))
Denominador común [src] 
         /                                      ___    \
  ___    |      2               x             \/ 7     |
\/ 7 *log|------------- + ------------- - -------------|
         |          ___             ___             ___|
         \2 + x + \/ 7    2 + x + \/ 7    2 + x + \/ 7 /
--------------------------------------------------------
                           14
7log⁡(xx+2+7−7x+2+7+2x+2+7)14\frac{\sqrt{7} \log{\left(\frac{x}{x + 2 + \sqrt{7}} - \frac{\sqrt{7}}{x + 2 + \sqrt{7}} + \frac{2}{x + 2 + \sqrt{7}} \right)}}{14} 
sqrt(7)*log(2/(2 + x + sqrt(7)) + x/(2 + x + sqrt(7)) - sqrt(7)/(2 + x + sqrt(7)))/14
Unión de expresiones racionales [src] 
         /          ___\
  ___    |2 + x - \/ 7 |
\/ 7 *log|-------------|
         |          ___|
         \2 + x + \/ 7 /
------------------------
           14
7log⁡(x−7+2x+2+7)14\frac{\sqrt{7} \log{\left(\frac{x - \sqrt{7} + 2}{x + 2 + \sqrt{7}} \right)}}{14} 
sqrt(7)*log((2 + x - sqrt(7))/(2 + x + sqrt(7)))/14
Denominador racional [src] 
         /  /          ___\\
  ___    |2*\2 + x - \/ 7 /|
\/ 7 *log|-----------------|
         |        ___      |
         \4 + 2*\/ 7  + 2*x/
----------------------------
             14
7log⁡(2(x−7+2)2x+(4+27))14\frac{\sqrt{7} \log{\left(\frac{2 \left(x - \sqrt{7} + 2\right)}{2 x + \left(4 + 2 \sqrt{7}\right)} \right)}}{14} 
sqrt(7)*log(2*(2 + x - sqrt(7))/(4 + 2*sqrt(7) + 2*x))/14
Abrimos la expresión [src] 
         /          ___    \
  ___    |2*x - 2*\/ 7  + 4|
\/ 7 *log|-----------------|
         |        ___      |
         \4 + 2*\/ 7  + 2*x/
----------------------------
             14
7log⁡((2x−27)+42x+(4+27))14\frac{\sqrt{7} \log{\left(\frac{\left(2 x - 2 \sqrt{7}\right) + 4}{2 x + \left(4 + 2 \sqrt{7}\right)} \right)}}{14} 
sqrt(7)*log((2*x - 2*sqrt(7) + 4)/(4 + 2*sqrt(7) + 2*x))/14
Compilar la expresión [src] 
         /          ___    \
  ___    |2*x - 2*\/ 7  + 4|
\/ 7 *log|-----------------|
         |        ___      |
         \4 + 2*\/ 7  + 2*x/
----------------------------
             14
7log⁡((2x−27)+42x+(4+27))14\frac{\sqrt{7} \log{\left(\frac{\left(2 x - 2 \sqrt{7}\right) + 4}{2 x + \left(4 + 2 \sqrt{7}\right)} \right)}}{14} 
sqrt(7)*log((2*x - 2*sqrt(7) + 4)/(4 + 2*sqrt(7) + 2*x))/14
Combinatoria [src] 
         /                             ___                         \
  ___    |        4                2*\/ 7                2*x       |
\/ 7 *log|----------------- - ----------------- + -----------------|
         |              ___                 ___                 ___|
         \4 + 2*x + 2*\/ 7    4 + 2*x + 2*\/ 7    4 + 2*x + 2*\/ 7 /
--------------------------------------------------------------------
                                 14
7log⁡(2x2x+4+27−272x+4+27+42x+4+27)14\frac{\sqrt{7} \log{\left(\frac{2 x}{2 x + 4 + 2 \sqrt{7}} - \frac{2 \sqrt{7}}{2 x + 4 + 2 \sqrt{7}} + \frac{4}{2 x + 4 + 2 \sqrt{7}} \right)}}{14} 
sqrt(7)*log(4/(4 + 2*x + 2*sqrt(7)) - 2*sqrt(7)/(4 + 2*x + 2*sqrt(7)) + 2*x/(4 + 2*x + 2*sqrt(7)))/14
Parte trigonométrica [src] 
         /        ___      \
  ___    |4 - 2*\/ 7  + 2*x|
\/ 7 *log|-----------------|
         |              ___|
         \4 + 2*x + 2*\/ 7 /
----------------------------
             14
7log⁡(2x−27+42x+4+27)14\frac{\sqrt{7} \log{\left(\frac{2 x - 2 \sqrt{7} + 4}{2 x + 4 + 2 \sqrt{7}} \right)}}{14} 
sqrt(7)*log((4 - 2*sqrt(7) + 2*x)/(4 + 2*x + 2*sqrt(7)))/14
Potencias [src] 
         /        ___      \
  ___    |4 - 2*\/ 7  + 2*x|
\/ 7 *log|-----------------|
         |              ___|
         \4 + 2*x + 2*\/ 7 /
----------------------------
             14
7log⁡(2x−27+42x+4+27)14\frac{\sqrt{7} \log{\left(\frac{2 x - 2 \sqrt{7} + 4}{2 x + 4 + 2 \sqrt{7}} \right)}}{14} 
sqrt(7)*log((4 - 2*sqrt(7) + 2*x)/(4 + 2*x + 2*sqrt(7)))/14
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