Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ log((10*x-6*sqrt(5))/(10*x+6*sqrt(5)))/(6*sqrt(5))

¿Cómo vas a descomponer esta log((10*x-6*sqrt(5))/(10*x+6*sqrt(5)))/(6*sqrt(5)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /           ___\
   |10*x - 6*\/ 5 |
log|--------------|
   |           ___|
   \10*x + 6*\/ 5 /
-------------------
          ___      
      6*\/ 5
$$\frac{\log{\left(\frac{10 x - 6 \sqrt{5}}{10 x + 6 \sqrt{5}} \right)}}{6 \sqrt{5}}$$ 
log((10*x - 6*sqrt(5))/(10*x + 6*sqrt(5)))/((6*sqrt(5)))
Descomposición de una fracción [src] 
sqrt(5)*log(-6*sqrt(5)/(10*x + 6*sqrt(5)) + 10*x/(10*x + 6*sqrt(5)))/30
$$\frac{\sqrt{5} \log{\left(\frac{10 x}{10 x + 6 \sqrt{5}} - \frac{6 \sqrt{5}}{10 x + 6 \sqrt{5}} \right)}}{30}$$ 
         /         ___                     \
  ___    |     6*\/ 5             10*x     |
\/ 5 *log|- -------------- + --------------|
         |             ___              ___|
         \  10*x + 6*\/ 5    10*x + 6*\/ 5 /
--------------------------------------------
                     30
Simplificación general [src] 
         /      ___      \
  ___    |- 3*\/ 5  + 5*x|
\/ 5 *log|---------------|
         |     ___       |
         \ 3*\/ 5  + 5*x /
--------------------------
            30
$$\frac{\sqrt{5} \log{\left(\frac{5 x - 3 \sqrt{5}}{5 x + 3 \sqrt{5}} \right)}}{30}$$ 
sqrt(5)*log((-3*sqrt(5) + 5*x)/(3*sqrt(5) + 5*x))/30
Respuesta numérica [src] 
0.074535599249993*log((10*x - 6*sqrt(5))/(10*x + 6*sqrt(5)))
0.074535599249993*log((10*x - 6*sqrt(5))/(10*x + 6*sqrt(5)))
Denominador racional [src] 
         /       2         ___\
  ___    |9 + 5*x  - 6*x*\/ 5 |
\/ 5 *log|--------------------|
         |             2      |
         \     -9 + 5*x       /
-------------------------------
               30
$$\frac{\sqrt{5} \log{\left(\frac{5 x^{2} - 6 \sqrt{5} x + 9}{5 x^{2} - 9} \right)}}{30}$$ 
sqrt(5)*log((9 + 5*x^2 - 6*x*sqrt(5))/(-9 + 5*x^2))/30
Combinatoria [src] 
         /         ___                     \
  ___    |     6*\/ 5             10*x     |
\/ 5 *log|- -------------- + --------------|
         |      ___              ___       |
         \  6*\/ 5  + 10*x   6*\/ 5  + 10*x/
--------------------------------------------
                     30
$$\frac{\sqrt{5} \log{\left(\frac{10 x}{10 x + 6 \sqrt{5}} - \frac{6 \sqrt{5}}{10 x + 6 \sqrt{5}} \right)}}{30}$$ 
sqrt(5)*log(-6*sqrt(5)/(6*sqrt(5) + 10*x) + 10*x/(6*sqrt(5) + 10*x))/30
Denominador común [src] 
         /         ___                   \
  ___    |     3*\/ 5            5*x     |
\/ 5 *log|- ------------- + -------------|
         |      ___             ___      |
         \  3*\/ 5  + 5*x   3*\/ 5  + 5*x/
------------------------------------------
                    30
$$\frac{\sqrt{5} \log{\left(\frac{5 x}{5 x + 3 \sqrt{5}} - \frac{3 \sqrt{5}}{5 x + 3 \sqrt{5}} \right)}}{30}$$ 
sqrt(5)*log(-3*sqrt(5)/(3*sqrt(5) + 5*x) + 5*x/(3*sqrt(5) + 5*x))/30
Abrimos la expresión [src] 
         /           ___\
  ___    |10*x - 6*\/ 5 |
\/ 5 *log|--------------|
         |           ___|
         \10*x + 6*\/ 5 /
-------------------------
            30
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 6 \sqrt{5}}{10 x + 6 \sqrt{5}} \right)}}{30}$$ 
sqrt(5)*log((10*x - 6*sqrt(5))/(10*x + 6*sqrt(5)))/30
Unión de expresiones racionales [src] 
         /      ___      \
  ___    |- 3*\/ 5  + 5*x|
\/ 5 *log|---------------|
         |     ___       |
         \ 3*\/ 5  + 5*x /
--------------------------
            30
$$\frac{\sqrt{5} \log{\left(\frac{5 x - 3 \sqrt{5}}{5 x + 3 \sqrt{5}} \right)}}{30}$$ 
sqrt(5)*log((-3*sqrt(5) + 5*x)/(3*sqrt(5) + 5*x))/30
Parte trigonométrica [src] 
         /      ___       \
  ___    |- 6*\/ 5  + 10*x|
\/ 5 *log|----------------|
         |     ___        |
         \ 6*\/ 5  + 10*x /
---------------------------
             30
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 6 \sqrt{5}}{10 x + 6 \sqrt{5}} \right)}}{30}$$ 
sqrt(5)*log((-6*sqrt(5) + 10*x)/(6*sqrt(5) + 10*x))/30
Compilar la expresión [src] 
         /           ___\
  ___    |10*x - 6*\/ 5 |
\/ 5 *log|--------------|
         |           ___|
         \10*x + 6*\/ 5 /
-------------------------
            30
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 6 \sqrt{5}}{10 x + 6 \sqrt{5}} \right)}}{30}$$ 
sqrt(5)*log((10*x - 6*sqrt(5))/(10*x + 6*sqrt(5)))/30
Potencias [src] 
         /      ___       \
  ___    |- 6*\/ 5  + 10*x|
\/ 5 *log|----------------|
         |     ___        |
         \ 6*\/ 5  + 10*x /
---------------------------
             30
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 6 \sqrt{5}}{10 x + 6 \sqrt{5}} \right)}}{30}$$ 
sqrt(5)*log((-6*sqrt(5) + 10*x)/(6*sqrt(5) + 10*x))/30
    © Sr Examen