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Simplificación de expresiones/ Descomposición en fracciones simples/ log((2*x-2*sqrt(5))/(2*x+2*sqrt(5)))/(2*sqrt(5))

¿Cómo vas a descomponer esta log((2*x-2*sqrt(5))/(2*x+2*sqrt(5)))/(2*sqrt(5)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ___\
   |2*x - 2*\/ 5 |
log|-------------|
   |          ___|
   \2*x + 2*\/ 5 /
------------------
         ___      
     2*\/ 5
log⁡(2x−252x+25)25\frac{\log{\left(\frac{2 x - 2 \sqrt{5}}{2 x + 2 \sqrt{5}} \right)}}{2 \sqrt{5}} 
log((2*x - 2*sqrt(5))/(2*x + 2*sqrt(5)))/((2*sqrt(5)))
Simplificación general [src] 
         /      ___\
  ___    |x - \/ 5 |
\/ 5 *log|---------|
         |      ___|
         \x + \/ 5 /
--------------------
         10
5log⁡(x−5x+5)10\frac{\sqrt{5} \log{\left(\frac{x - \sqrt{5}}{x + \sqrt{5}} \right)}}{10} 
sqrt(5)*log((x - sqrt(5))/(x + sqrt(5)))/10
Descomposición de una fracción [src] 
sqrt(5)*log(-2*sqrt(5)/(2*x + 2*sqrt(5)) + 2*x/(2*x + 2*sqrt(5)))/10
5log⁡(2x2x+25−252x+25)10\frac{\sqrt{5} \log{\left(\frac{2 x}{2 x + 2 \sqrt{5}} - \frac{2 \sqrt{5}}{2 x + 2 \sqrt{5}} \right)}}{10} 
         /         ___                   \
  ___    |     2*\/ 5            2*x     |
\/ 5 *log|- ------------- + -------------|
         |            ___             ___|
         \  2*x + 2*\/ 5    2*x + 2*\/ 5 /
------------------------------------------
                    10
Respuesta numérica [src] 
0.223606797749979*log((2*x - 2*sqrt(5))/(2*x + 2*sqrt(5)))
0.223606797749979*log((2*x - 2*sqrt(5))/(2*x + 2*sqrt(5)))
Denominador racional [src] 
         /     2         ___\
  ___    |5 + x  - 2*x*\/ 5 |
\/ 5 *log|------------------|
         |           2      |
         \     -5 + x       /
-----------------------------
              10
5log⁡(x2−25x+5x2−5)10\frac{\sqrt{5} \log{\left(\frac{x^{2} - 2 \sqrt{5} x + 5}{x^{2} - 5} \right)}}{10} 
sqrt(5)*log((5 + x^2 - 2*x*sqrt(5))/(-5 + x^2))/10
Denominador común [src] 
         /                ___  \
  ___    |    x         \/ 5   |
\/ 5 *log|--------- - ---------|
         |      ___         ___|
         \x + \/ 5    x + \/ 5 /
--------------------------------
               10
5log⁡(xx+5−5x+5)10\frac{\sqrt{5} \log{\left(\frac{x}{x + \sqrt{5}} - \frac{\sqrt{5}}{x + \sqrt{5}} \right)}}{10} 
sqrt(5)*log(x/(x + sqrt(5)) - sqrt(5)/(x + sqrt(5)))/10
Unión de expresiones racionales [src] 
         /      ___\
  ___    |x - \/ 5 |
\/ 5 *log|---------|
         |      ___|
         \x + \/ 5 /
--------------------
         10
5log⁡(x−5x+5)10\frac{\sqrt{5} \log{\left(\frac{x - \sqrt{5}}{x + \sqrt{5}} \right)}}{10} 
sqrt(5)*log((x - sqrt(5))/(x + sqrt(5)))/10
Combinatoria [src] 
         /         ___                   \
  ___    |     2*\/ 5            2*x     |
\/ 5 *log|- ------------- + -------------|
         |            ___             ___|
         \  2*x + 2*\/ 5    2*x + 2*\/ 5 /
------------------------------------------
                    10
5log⁡(2x2x+25−252x+25)10\frac{\sqrt{5} \log{\left(\frac{2 x}{2 x + 2 \sqrt{5}} - \frac{2 \sqrt{5}}{2 x + 2 \sqrt{5}} \right)}}{10} 
sqrt(5)*log(-2*sqrt(5)/(2*x + 2*sqrt(5)) + 2*x/(2*x + 2*sqrt(5)))/10
Potencias [src] 
         /      ___      \
  ___    |- 2*\/ 5  + 2*x|
\/ 5 *log|---------------|
         |           ___ |
         \ 2*x + 2*\/ 5  /
--------------------------
            10
5log⁡(2x−252x+25)10\frac{\sqrt{5} \log{\left(\frac{2 x - 2 \sqrt{5}}{2 x + 2 \sqrt{5}} \right)}}{10} 
sqrt(5)*log((-2*sqrt(5) + 2*x)/(2*x + 2*sqrt(5)))/10
Parte trigonométrica [src] 
         /      ___      \
  ___    |- 2*\/ 5  + 2*x|
\/ 5 *log|---------------|
         |           ___ |
         \ 2*x + 2*\/ 5  /
--------------------------
            10
5log⁡(2x−252x+25)10\frac{\sqrt{5} \log{\left(\frac{2 x - 2 \sqrt{5}}{2 x + 2 \sqrt{5}} \right)}}{10} 
sqrt(5)*log((-2*sqrt(5) + 2*x)/(2*x + 2*sqrt(5)))/10
Abrimos la expresión [src] 
         /          ___\
  ___    |2*x - 2*\/ 5 |
\/ 5 *log|-------------|
         |          ___|
         \2*x + 2*\/ 5 /
------------------------
           10
5log⁡(2x−252x+25)10\frac{\sqrt{5} \log{\left(\frac{2 x - 2 \sqrt{5}}{2 x + 2 \sqrt{5}} \right)}}{10} 
sqrt(5)*log((2*x - 2*sqrt(5))/(2*x + 2*sqrt(5)))/10
Compilar la expresión [src] 
         /          ___\
  ___    |2*x - 2*\/ 5 |
\/ 5 *log|-------------|
         |          ___|
         \2*x + 2*\/ 5 /
------------------------
           10
5log⁡(2x−252x+25)10\frac{\sqrt{5} \log{\left(\frac{2 x - 2 \sqrt{5}}{2 x + 2 \sqrt{5}} \right)}}{10} 
sqrt(5)*log((2*x - 2*sqrt(5))/(2*x + 2*sqrt(5)))/10
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