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Simplificación de expresiones/ Descomposición en fracciones simples/ log((10*x-2*sqrt(35))/(10*x+2*sqrt(35)))/(2*sqrt(35))

¿Cómo vas a descomponer esta log((10*x-2*sqrt(35))/(10*x+2*sqrt(35)))/(2*sqrt(35)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /           ____\
   |10*x - 2*\/ 35 |
log|---------------|
   |           ____|
   \10*x + 2*\/ 35 /
--------------------
          ____      
      2*\/ 35
$$\frac{\log{\left(\frac{10 x - 2 \sqrt{35}}{10 x + 2 \sqrt{35}} \right)}}{2 \sqrt{35}}$$ 
log((10*x - 2*sqrt(35))/(10*x + 2*sqrt(35)))/((2*sqrt(35)))
Descomposición de una fracción [src] 
sqrt(35)*log(-2*sqrt(35)/(10*x + 2*sqrt(35)) + 10*x/(10*x + 2*sqrt(35)))/70
$$\frac{\sqrt{35} \log{\left(\frac{10 x}{10 x + 2 \sqrt{35}} - \frac{2 \sqrt{35}}{10 x + 2 \sqrt{35}} \right)}}{70}$$ 
          /          ____                     \
  ____    |      2*\/ 35             10*x     |
\/ 35 *log|- --------------- + ---------------|
          |             ____              ____|
          \  10*x + 2*\/ 35    10*x + 2*\/ 35 /
-----------------------------------------------
                       70
Simplificación general [src] 
          /    ____      \
  ____    |- \/ 35  + 5*x|
\/ 35 *log|--------------|
          |   ____       |
          \ \/ 35  + 5*x /
--------------------------
            70
$$\frac{\sqrt{35} \log{\left(\frac{5 x - \sqrt{35}}{5 x + \sqrt{35}} \right)}}{70}$$ 
sqrt(35)*log((-sqrt(35) + 5*x)/(sqrt(35) + 5*x))/70
Parte trigonométrica [src] 
          /      ____       \
  ____    |- 2*\/ 35  + 10*x|
\/ 35 *log|-----------------|
          |     ____        |
          \ 2*\/ 35  + 10*x /
-----------------------------
              70
$$\frac{\sqrt{35} \log{\left(\frac{10 x - 2 \sqrt{35}}{10 x + 2 \sqrt{35}} \right)}}{70}$$ 
sqrt(35)*log((-2*sqrt(35) + 10*x)/(2*sqrt(35) + 10*x))/70
Potencias [src] 
          /      ____       \
  ____    |- 2*\/ 35  + 10*x|
\/ 35 *log|-----------------|
          |     ____        |
          \ 2*\/ 35  + 10*x /
-----------------------------
              70
$$\frac{\sqrt{35} \log{\left(\frac{10 x - 2 \sqrt{35}}{10 x + 2 \sqrt{35}} \right)}}{70}$$ 
sqrt(35)*log((-2*sqrt(35) + 10*x)/(2*sqrt(35) + 10*x))/70
Unión de expresiones racionales [src] 
          /    ____      \
  ____    |- \/ 35  + 5*x|
\/ 35 *log|--------------|
          |   ____       |
          \ \/ 35  + 5*x /
--------------------------
            70
$$\frac{\sqrt{35} \log{\left(\frac{5 x - \sqrt{35}}{5 x + \sqrt{35}} \right)}}{70}$$ 
sqrt(35)*log((-sqrt(35) + 5*x)/(sqrt(35) + 5*x))/70
Combinatoria [src] 
          /          ____                     \
  ____    |      2*\/ 35             10*x     |
\/ 35 *log|- --------------- + ---------------|
          |      ____              ____       |
          \  2*\/ 35  + 10*x   2*\/ 35  + 10*x/
-----------------------------------------------
                       70
$$\frac{\sqrt{35} \log{\left(\frac{10 x}{10 x + 2 \sqrt{35}} - \frac{2 \sqrt{35}}{10 x + 2 \sqrt{35}} \right)}}{70}$$ 
sqrt(35)*log(-2*sqrt(35)/(2*sqrt(35) + 10*x) + 10*x/(2*sqrt(35) + 10*x))/70
Respuesta numérica [src] 
0.0845154254728517*log((10*x - 2*sqrt(35))/(10*x + 2*sqrt(35)))
0.0845154254728517*log((10*x - 2*sqrt(35))/(10*x + 2*sqrt(35)))
Compilar la expresión [src] 
          /           ____\
  ____    |10*x - 2*\/ 35 |
\/ 35 *log|---------------|
          |           ____|
          \10*x + 2*\/ 35 /
---------------------------
             70
$$\frac{\sqrt{35} \log{\left(\frac{10 x - 2 \sqrt{35}}{10 x + 2 \sqrt{35}} \right)}}{70}$$ 
sqrt(35)*log((10*x - 2*sqrt(35))/(10*x + 2*sqrt(35)))/70
Denominador racional [src] 
          /       2         ____\
  ____    |7 + 5*x  - 2*x*\/ 35 |
\/ 35 *log|---------------------|
          |              2      |
          \      -7 + 5*x       /
---------------------------------
                70
$$\frac{\sqrt{35} \log{\left(\frac{5 x^{2} - 2 \sqrt{35} x + 7}{5 x^{2} - 7} \right)}}{70}$$ 
sqrt(35)*log((7 + 5*x^2 - 2*x*sqrt(35))/(-7 + 5*x^2))/70
Denominador común [src] 
          /       ____                  \
  ____    |     \/ 35           5*x     |
\/ 35 *log|- ------------ + ------------|
          |    ____           ____      |
          \  \/ 35  + 5*x   \/ 35  + 5*x/
-----------------------------------------
                    70
$$\frac{\sqrt{35} \log{\left(\frac{5 x}{5 x + \sqrt{35}} - \frac{\sqrt{35}}{5 x + \sqrt{35}} \right)}}{70}$$ 
sqrt(35)*log(-sqrt(35)/(sqrt(35) + 5*x) + 5*x/(sqrt(35) + 5*x))/70
Abrimos la expresión [src] 
          /           ____\
  ____    |10*x - 2*\/ 35 |
\/ 35 *log|---------------|
          |           ____|
          \10*x + 2*\/ 35 /
---------------------------
             70
$$\frac{\sqrt{35} \log{\left(\frac{10 x - 2 \sqrt{35}}{10 x + 2 \sqrt{35}} \right)}}{70}$$ 
sqrt(35)*log((10*x - 2*sqrt(35))/(10*x + 2*sqrt(35)))/70
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