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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   /           ____\
   |10*x - 2*\/ 10 |
log|---------------|
   |    ____       |
   \2*\/ 10  + 10*x/
--------------------
          ____      
      2*\/ 10
$$\frac{\log{\left(\frac{10 x - 2 \sqrt{10}}{10 x + 2 \sqrt{10}} \right)}}{2 \sqrt{10}}$$ 
log((10*x - 2*sqrt(10))/(2*sqrt(10) + 10*x))/((2*sqrt(10)))
Descomposición de una fracción [src] 
sqrt(10)*log(-2*sqrt(10)/(2*sqrt(10) + 10*x) + 10*x/(2*sqrt(10) + 10*x))/20
$$\frac{\sqrt{10} \log{\left(\frac{10 x}{10 x + 2 \sqrt{10}} - \frac{2 \sqrt{10}}{10 x + 2 \sqrt{10}} \right)}}{20}$$ 
          /          ____                     \
  ____    |      2*\/ 10             10*x     |
\/ 10 *log|- --------------- + ---------------|
          |      ____              ____       |
          \  2*\/ 10  + 10*x   2*\/ 10  + 10*x/
-----------------------------------------------
                       20
Simplificación general [src] 
          /    ____      \
  ____    |- \/ 10  + 5*x|
\/ 10 *log|--------------|
          |   ____       |
          \ \/ 10  + 5*x /
--------------------------
            20
$$\frac{\sqrt{10} \log{\left(\frac{5 x - \sqrt{10}}{5 x + \sqrt{10}} \right)}}{20}$$ 
sqrt(10)*log((-sqrt(10) + 5*x)/(sqrt(10) + 5*x))/20
Respuesta numérica [src] 
0.158113883008419*log((10*x - 2*sqrt(10))/(2*sqrt(10) + 10*x))
0.158113883008419*log((10*x - 2*sqrt(10))/(2*sqrt(10) + 10*x))
Denominador racional [src] 
          /       2         ____\
  ____    |2 + 5*x  - 2*x*\/ 10 |
\/ 10 *log|---------------------|
          |              2      |
          \      -2 + 5*x       /
---------------------------------
                20
$$\frac{\sqrt{10} \log{\left(\frac{5 x^{2} - 2 \sqrt{10} x + 2}{5 x^{2} - 2} \right)}}{20}$$ 
sqrt(10)*log((2 + 5*x^2 - 2*x*sqrt(10))/(-2 + 5*x^2))/20
Combinatoria [src] 
          /          ____                     \
  ____    |      2*\/ 10             10*x     |
\/ 10 *log|- --------------- + ---------------|
          |      ____              ____       |
          \  2*\/ 10  + 10*x   2*\/ 10  + 10*x/
-----------------------------------------------
                       20
$$\frac{\sqrt{10} \log{\left(\frac{10 x}{10 x + 2 \sqrt{10}} - \frac{2 \sqrt{10}}{10 x + 2 \sqrt{10}} \right)}}{20}$$ 
sqrt(10)*log(-2*sqrt(10)/(2*sqrt(10) + 10*x) + 10*x/(2*sqrt(10) + 10*x))/20
Potencias [src] 
          /      ____       \
  ____    |- 2*\/ 10  + 10*x|
\/ 10 *log|-----------------|
          |     ____        |
          \ 2*\/ 10  + 10*x /
-----------------------------
              20
$$\frac{\sqrt{10} \log{\left(\frac{10 x - 2 \sqrt{10}}{10 x + 2 \sqrt{10}} \right)}}{20}$$ 
sqrt(10)*log((-2*sqrt(10) + 10*x)/(2*sqrt(10) + 10*x))/20
Parte trigonométrica [src] 
          /      ____       \
  ____    |- 2*\/ 10  + 10*x|
\/ 10 *log|-----------------|
          |     ____        |
          \ 2*\/ 10  + 10*x /
-----------------------------
              20
$$\frac{\sqrt{10} \log{\left(\frac{10 x - 2 \sqrt{10}}{10 x + 2 \sqrt{10}} \right)}}{20}$$ 
sqrt(10)*log((-2*sqrt(10) + 10*x)/(2*sqrt(10) + 10*x))/20
Unión de expresiones racionales [src] 
          /    ____      \
  ____    |- \/ 10  + 5*x|
\/ 10 *log|--------------|
          |   ____       |
          \ \/ 10  + 5*x /
--------------------------
            20
$$\frac{\sqrt{10} \log{\left(\frac{5 x - \sqrt{10}}{5 x + \sqrt{10}} \right)}}{20}$$ 
sqrt(10)*log((-sqrt(10) + 5*x)/(sqrt(10) + 5*x))/20
Abrimos la expresión [src] 
          /           ____\
  ____    |10*x - 2*\/ 10 |
\/ 10 *log|---------------|
          |    ____       |
          \2*\/ 10  + 10*x/
---------------------------
             20
$$\frac{\sqrt{10} \log{\left(\frac{10 x - 2 \sqrt{10}}{10 x + 2 \sqrt{10}} \right)}}{20}$$ 
sqrt(10)*log((10*x - 2*sqrt(10))/(2*sqrt(10) + 10*x))/20
Compilar la expresión [src] 
          /           ____\
  ____    |10*x - 2*\/ 10 |
\/ 10 *log|---------------|
          |    ____       |
          \2*\/ 10  + 10*x/
---------------------------
             20
$$\frac{\sqrt{10} \log{\left(\frac{10 x - 2 \sqrt{10}}{10 x + 2 \sqrt{10}} \right)}}{20}$$ 
sqrt(10)*log((10*x - 2*sqrt(10))/(2*sqrt(10) + 10*x))/20
Denominador común [src] 
          /       ____                  \
  ____    |     \/ 10           5*x     |
\/ 10 *log|- ------------ + ------------|
          |    ____           ____      |
          \  \/ 10  + 5*x   \/ 10  + 5*x/
-----------------------------------------
                    20
$$\frac{\sqrt{10} \log{\left(\frac{5 x}{5 x + \sqrt{10}} - \frac{\sqrt{10}}{5 x + \sqrt{10}} \right)}}{20}$$ 
sqrt(10)*log(-sqrt(10)/(sqrt(10) + 5*x) + 5*x/(sqrt(10) + 5*x))/20
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