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Simplificación de expresiones/ Descomposición en fracciones simples/ log((2*x-2*sqrt(13)+10)/(10+2*sqrt(13)+2*x))/(2*sqrt(13))

¿Cómo vas a descomponer esta log((2*x-2*sqrt(13)+10)/(10+2*sqrt(13)+2*x))/(2*sqrt(13)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ____     \
   |2*x - 2*\/ 13  + 10|
log|-------------------|
   |         ____      |
   \10 + 2*\/ 13  + 2*x/
------------------------
            ____        
        2*\/ 13
$$\frac{\log{\left(\frac{\left(2 x - 2 \sqrt{13}\right) + 10}{2 x + \left(2 \sqrt{13} + 10\right)} \right)}}{2 \sqrt{13}}$$ 
log((2*x - 2*sqrt(13) + 10)/(10 + 2*sqrt(13) + 2*x))/((2*sqrt(13)))
Simplificación general [src] 
          /          ____\
  ____    |5 + x - \/ 13 |
\/ 13 *log|--------------|
          |          ____|
          \5 + x + \/ 13 /
--------------------------
            26
$$\frac{\sqrt{13} \log{\left(\frac{x - \sqrt{13} + 5}{x + \sqrt{13} + 5} \right)}}{26}$$ 
sqrt(13)*log((5 + x - sqrt(13))/(5 + x + sqrt(13)))/26
Descomposición de una fracción [src] 
sqrt(13)*log(10/(10 + 2*sqrt(13) + 2*x) - 2*sqrt(13)/(10 + 2*sqrt(13) + 2*x) + 2*x/(10 + 2*sqrt(13) + 2*x))/26
$$\frac{\sqrt{13} \log{\left(\frac{2 x}{2 x + \left(2 \sqrt{13} + 10\right)} - \frac{2 \sqrt{13}}{2 x + \left(2 \sqrt{13} + 10\right)} + \frac{10}{2 x + \left(2 \sqrt{13} + 10\right)} \right)}}{26}$$ 
          /                                ____                           \
  ____    |         10                 2*\/ 13                 2*x        |
\/ 13 *log|------------------- - ------------------- + -------------------|
          |         ____                  ____                  ____      |
          \10 + 2*\/ 13  + 2*x   10 + 2*\/ 13  + 2*x   10 + 2*\/ 13  + 2*x/
---------------------------------------------------------------------------
                                     26
Respuesta numérica [src] 
0.138675049056307*log((2*x - 2*sqrt(13) + 10)/(10 + 2*sqrt(13) + 2*x))
0.138675049056307*log((2*x - 2*sqrt(13) + 10)/(10 + 2*sqrt(13) + 2*x))
Denominador común [src] 
          /                                        ____    \
  ____    |      5                x              \/ 13     |
\/ 13 *log|-------------- + -------------- - --------------|
          |          ____             ____             ____|
          \5 + x + \/ 13    5 + x + \/ 13    5 + x + \/ 13 /
------------------------------------------------------------
                             26
$$\frac{\sqrt{13} \log{\left(\frac{x}{x + \sqrt{13} + 5} - \frac{\sqrt{13}}{x + \sqrt{13} + 5} + \frac{5}{x + \sqrt{13} + 5} \right)}}{26}$$ 
sqrt(13)*log(5/(5 + x + sqrt(13)) + x/(5 + x + sqrt(13)) - sqrt(13)/(5 + x + sqrt(13)))/26
Potencias [src] 
          /         ____      \
  ____    |10 - 2*\/ 13  + 2*x|
\/ 13 *log|-------------------|
          |               ____|
          \10 + 2*x + 2*\/ 13 /
-------------------------------
               26
$$\frac{\sqrt{13} \log{\left(\frac{2 x - 2 \sqrt{13} + 10}{2 x + 2 \sqrt{13} + 10} \right)}}{26}$$ 
sqrt(13)*log((10 - 2*sqrt(13) + 2*x)/(10 + 2*x + 2*sqrt(13)))/26
Denominador racional [src] 
          /   /          ____\\
  ____    | 2*\5 + x - \/ 13 /|
\/ 13 *log|-------------------|
          |         ____      |
          \10 + 2*\/ 13  + 2*x/
-------------------------------
               26
$$\frac{\sqrt{13} \log{\left(\frac{2 \left(x - \sqrt{13} + 5\right)}{2 x + \left(2 \sqrt{13} + 10\right)} \right)}}{26}$$ 
sqrt(13)*log(2*(5 + x - sqrt(13))/(10 + 2*sqrt(13) + 2*x))/26
Combinatoria [src] 
          /                                ____                           \
  ____    |         10                 2*\/ 13                 2*x        |
\/ 13 *log|------------------- - ------------------- + -------------------|
          |               ____                  ____                  ____|
          \10 + 2*x + 2*\/ 13    10 + 2*x + 2*\/ 13    10 + 2*x + 2*\/ 13 /
---------------------------------------------------------------------------
                                     26
$$\frac{\sqrt{13} \log{\left(\frac{2 x}{2 x + 2 \sqrt{13} + 10} - \frac{2 \sqrt{13}}{2 x + 2 \sqrt{13} + 10} + \frac{10}{2 x + 2 \sqrt{13} + 10} \right)}}{26}$$ 
sqrt(13)*log(10/(10 + 2*x + 2*sqrt(13)) - 2*sqrt(13)/(10 + 2*x + 2*sqrt(13)) + 2*x/(10 + 2*x + 2*sqrt(13)))/26
Unión de expresiones racionales [src] 
          /          ____\
  ____    |5 + x - \/ 13 |
\/ 13 *log|--------------|
          |          ____|
          \5 + x + \/ 13 /
--------------------------
            26
$$\frac{\sqrt{13} \log{\left(\frac{x - \sqrt{13} + 5}{x + \sqrt{13} + 5} \right)}}{26}$$ 
sqrt(13)*log((5 + x - sqrt(13))/(5 + x + sqrt(13)))/26
Abrimos la expresión [src] 
          /          ____     \
  ____    |2*x - 2*\/ 13  + 10|
\/ 13 *log|-------------------|
          |         ____      |
          \10 + 2*\/ 13  + 2*x/
-------------------------------
               26
$$\frac{\sqrt{13} \log{\left(\frac{\left(2 x - 2 \sqrt{13}\right) + 10}{2 x + \left(2 \sqrt{13} + 10\right)} \right)}}{26}$$ 
sqrt(13)*log((2*x - 2*sqrt(13) + 10)/(10 + 2*sqrt(13) + 2*x))/26
Compilar la expresión [src] 
          /          ____     \
  ____    |2*x - 2*\/ 13  + 10|
\/ 13 *log|-------------------|
          |         ____      |
          \10 + 2*\/ 13  + 2*x/
-------------------------------
               26
$$\frac{\sqrt{13} \log{\left(\frac{\left(2 x - 2 \sqrt{13}\right) + 10}{2 x + \left(2 \sqrt{13} + 10\right)} \right)}}{26}$$ 
sqrt(13)*log((2*x - 2*sqrt(13) + 10)/(10 + 2*sqrt(13) + 2*x))/26
Parte trigonométrica [src] 
          /         ____      \
  ____    |10 - 2*\/ 13  + 2*x|
\/ 13 *log|-------------------|
          |               ____|
          \10 + 2*x + 2*\/ 13 /
-------------------------------
               26
$$\frac{\sqrt{13} \log{\left(\frac{2 x - 2 \sqrt{13} + 10}{2 x + 2 \sqrt{13} + 10} \right)}}{26}$$ 
sqrt(13)*log((10 - 2*sqrt(13) + 2*x)/(10 + 2*x + 2*sqrt(13)))/26
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