Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ log((10*x-4*sqrt(5))/(4*sqrt(5)+10*x))/(4*sqrt(5))

¿Cómo vas a descomponer esta log((10*x-4*sqrt(5))/(4*sqrt(5)+10*x))/(4*sqrt(5)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /           ___\
   |10*x - 4*\/ 5 |
log|--------------|
   |    ___       |
   \4*\/ 5  + 10*x/
-------------------
          ___      
      4*\/ 5
$$\frac{\log{\left(\frac{10 x - 4 \sqrt{5}}{10 x + 4 \sqrt{5}} \right)}}{4 \sqrt{5}}$$ 
log((10*x - 4*sqrt(5))/(4*sqrt(5) + 10*x))/((4*sqrt(5)))
Simplificación general [src] 
         /      ___      \
  ___    |- 2*\/ 5  + 5*x|
\/ 5 *log|---------------|
         |     ___       |
         \ 2*\/ 5  + 5*x /
--------------------------
            20
$$\frac{\sqrt{5} \log{\left(\frac{5 x - 2 \sqrt{5}}{5 x + 2 \sqrt{5}} \right)}}{20}$$ 
sqrt(5)*log((-2*sqrt(5) + 5*x)/(2*sqrt(5) + 5*x))/20
Descomposición de una fracción [src] 
sqrt(5)*log(-4*sqrt(5)/(4*sqrt(5) + 10*x) + 10*x/(4*sqrt(5) + 10*x))/20
$$\frac{\sqrt{5} \log{\left(\frac{10 x}{10 x + 4 \sqrt{5}} - \frac{4 \sqrt{5}}{10 x + 4 \sqrt{5}} \right)}}{20}$$ 
         /         ___                     \
  ___    |     4*\/ 5             10*x     |
\/ 5 *log|- -------------- + --------------|
         |      ___              ___       |
         \  4*\/ 5  + 10*x   4*\/ 5  + 10*x/
--------------------------------------------
                     20
Respuesta numérica [src] 
0.111803398874989*log((10*x - 4*sqrt(5))/(4*sqrt(5) + 10*x))
0.111803398874989*log((10*x - 4*sqrt(5))/(4*sqrt(5) + 10*x))
Denominador común [src] 
         /         ___                   \
  ___    |     2*\/ 5            5*x     |
\/ 5 *log|- ------------- + -------------|
         |      ___             ___      |
         \  2*\/ 5  + 5*x   2*\/ 5  + 5*x/
------------------------------------------
                    20
$$\frac{\sqrt{5} \log{\left(\frac{5 x}{5 x + 2 \sqrt{5}} - \frac{2 \sqrt{5}}{5 x + 2 \sqrt{5}} \right)}}{20}$$ 
sqrt(5)*log(-2*sqrt(5)/(2*sqrt(5) + 5*x) + 5*x/(2*sqrt(5) + 5*x))/20
Parte trigonométrica [src] 
         /      ___       \
  ___    |- 4*\/ 5  + 10*x|
\/ 5 *log|----------------|
         |     ___        |
         \ 4*\/ 5  + 10*x /
---------------------------
             20
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 4 \sqrt{5}}{10 x + 4 \sqrt{5}} \right)}}{20}$$ 
sqrt(5)*log((-4*sqrt(5) + 10*x)/(4*sqrt(5) + 10*x))/20
Combinatoria [src] 
         /         ___                     \
  ___    |     4*\/ 5             10*x     |
\/ 5 *log|- -------------- + --------------|
         |      ___              ___       |
         \  4*\/ 5  + 10*x   4*\/ 5  + 10*x/
--------------------------------------------
                     20
$$\frac{\sqrt{5} \log{\left(\frac{10 x}{10 x + 4 \sqrt{5}} - \frac{4 \sqrt{5}}{10 x + 4 \sqrt{5}} \right)}}{20}$$ 
sqrt(5)*log(-4*sqrt(5)/(4*sqrt(5) + 10*x) + 10*x/(4*sqrt(5) + 10*x))/20
Unión de expresiones racionales [src] 
         /      ___      \
  ___    |- 2*\/ 5  + 5*x|
\/ 5 *log|---------------|
         |     ___       |
         \ 2*\/ 5  + 5*x /
--------------------------
            20
$$\frac{\sqrt{5} \log{\left(\frac{5 x - 2 \sqrt{5}}{5 x + 2 \sqrt{5}} \right)}}{20}$$ 
sqrt(5)*log((-2*sqrt(5) + 5*x)/(2*sqrt(5) + 5*x))/20
Potencias [src] 
         /      ___       \
  ___    |- 4*\/ 5  + 10*x|
\/ 5 *log|----------------|
         |     ___        |
         \ 4*\/ 5  + 10*x /
---------------------------
             20
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 4 \sqrt{5}}{10 x + 4 \sqrt{5}} \right)}}{20}$$ 
sqrt(5)*log((-4*sqrt(5) + 10*x)/(4*sqrt(5) + 10*x))/20
Compilar la expresión [src] 
         /           ___\
  ___    |10*x - 4*\/ 5 |
\/ 5 *log|--------------|
         |    ___       |
         \4*\/ 5  + 10*x/
-------------------------
            20
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 4 \sqrt{5}}{10 x + 4 \sqrt{5}} \right)}}{20}$$ 
sqrt(5)*log((10*x - 4*sqrt(5))/(4*sqrt(5) + 10*x))/20
Abrimos la expresión [src] 
         /           ___\
  ___    |10*x - 4*\/ 5 |
\/ 5 *log|--------------|
         |    ___       |
         \4*\/ 5  + 10*x/
-------------------------
            20
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 4 \sqrt{5}}{10 x + 4 \sqrt{5}} \right)}}{20}$$ 
sqrt(5)*log((10*x - 4*sqrt(5))/(4*sqrt(5) + 10*x))/20
Denominador racional [src] 
         /       2         ___\
  ___    |4 + 5*x  - 4*x*\/ 5 |
\/ 5 *log|--------------------|
         |             2      |
         \     -4 + 5*x       /
-------------------------------
               20
$$\frac{\sqrt{5} \log{\left(\frac{5 x^{2} - 4 \sqrt{5} x + 4}{5 x^{2} - 4} \right)}}{20}$$ 
sqrt(5)*log((4 + 5*x^2 - 4*x*sqrt(5))/(-4 + 5*x^2))/20
    © Sr Examen