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Simplificación de expresiones/ Descomposición en fracciones simples/ log((2*x-sqrt(141)-11)/((-11)+sqrt(141)+2*x))/sqrt(141)

¿Cómo vas a descomponer esta log((2*x-sqrt(141)-11)/((-11)+sqrt(141)+2*x))/sqrt(141) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /         _____     \
   | 2*x - \/ 141  - 11|
log|-------------------|
   |        _____      |
   \-11 + \/ 141  + 2*x/
------------------------
          _____         
        \/ 141
log⁡((2x−141)−112x+(−11+141))141\frac{\log{\left(\frac{\left(2 x - \sqrt{141}\right) - 11}{2 x + \left(-11 + \sqrt{141}\right)} \right)}}{\sqrt{141}} 
log((2*x - sqrt(141) - 11)/(-11 + sqrt(141) + 2*x))/sqrt(141)
Descomposición de una fracción [src] 
sqrt(141)*log(-11/(-11 + sqrt(141) + 2*x) - sqrt(141)/(-11 + sqrt(141) + 2*x) + 2*x/(-11 + sqrt(141) + 2*x))/141
141log⁡(2x2x+(−11+141)−1412x+(−11+141)−112x+(−11+141))141\frac{\sqrt{141} \log{\left(\frac{2 x}{2 x + \left(-11 + \sqrt{141}\right)} - \frac{\sqrt{141}}{2 x + \left(-11 + \sqrt{141}\right)} - \frac{11}{2 x + \left(-11 + \sqrt{141}\right)} \right)}}{141} 
           /                                _____                            \
  _____    |           11                 \/ 141                  2*x        |
\/ 141 *log|- ------------------- - ------------------- + -------------------|
           |          _____                 _____                 _____      |
           \  -11 + \/ 141  + 2*x   -11 + \/ 141  + 2*x   -11 + \/ 141  + 2*x/
------------------------------------------------------------------------------
                                     141
Simplificación general [src] 
           /        _____      \
  _____    |-11 - \/ 141  + 2*x|
\/ 141 *log|-------------------|
           |        _____      |
           \-11 + \/ 141  + 2*x/
--------------------------------
              141
141log⁡(2x−141−112x−11+141)141\frac{\sqrt{141} \log{\left(\frac{2 x - \sqrt{141} - 11}{2 x - 11 + \sqrt{141}} \right)}}{141} 
sqrt(141)*log((-11 - sqrt(141) + 2*x)/(-11 + sqrt(141) + 2*x))/141
Unión de expresiones racionales [src] 
           /        _____      \
  _____    |-11 - \/ 141  + 2*x|
\/ 141 *log|-------------------|
           |        _____      |
           \-11 + \/ 141  + 2*x/
--------------------------------
              141
141log⁡(2x−141−112x−11+141)141\frac{\sqrt{141} \log{\left(\frac{2 x - \sqrt{141} - 11}{2 x - 11 + \sqrt{141}} \right)}}{141} 
sqrt(141)*log((-11 - sqrt(141) + 2*x)/(-11 + sqrt(141) + 2*x))/141
Respuesta numérica [src] 
0.0842151921066519*log((2*x - sqrt(141) - 11)/(-11 + sqrt(141) + 2*x))
0.0842151921066519*log((2*x - sqrt(141) - 11)/(-11 + sqrt(141) + 2*x))
Combinatoria [src] 
           /                                _____                            \
  _____    |           11                 \/ 141                  2*x        |
\/ 141 *log|- ------------------- - ------------------- + -------------------|
           |          _____                 _____                 _____      |
           \  -11 + \/ 141  + 2*x   -11 + \/ 141  + 2*x   -11 + \/ 141  + 2*x/
------------------------------------------------------------------------------
                                     141
141log⁡(2x2x−11+141−1412x−11+141−112x−11+141)141\frac{\sqrt{141} \log{\left(\frac{2 x}{2 x - 11 + \sqrt{141}} - \frac{\sqrt{141}}{2 x - 11 + \sqrt{141}} - \frac{11}{2 x - 11 + \sqrt{141}} \right)}}{141} 
sqrt(141)*log(-11/(-11 + sqrt(141) + 2*x) - sqrt(141)/(-11 + sqrt(141) + 2*x) + 2*x/(-11 + sqrt(141) + 2*x))/141
Denominador racional [src] 
           / /       _____      \ \
  _____    |-\11 + \/ 141  - 2*x/ |
\/ 141 *log|----------------------|
           |         _____        |
           \ -11 + \/ 141  + 2*x  /
-----------------------------------
                141
141log⁡(−−2x+11+1412x−11+141)141\frac{\sqrt{141} \log{\left(- \frac{- 2 x + 11 + \sqrt{141}}{2 x - 11 + \sqrt{141}} \right)}}{141} 
sqrt(141)*log(-(11 + sqrt(141) - 2*x)/(-11 + sqrt(141) + 2*x))/141
Denominador común [src] 
           /                                _____                            \
  _____    |           11                 \/ 141                  2*x        |
\/ 141 *log|- ------------------- - ------------------- + -------------------|
           |          _____                 _____                 _____      |
           \  -11 + \/ 141  + 2*x   -11 + \/ 141  + 2*x   -11 + \/ 141  + 2*x/
------------------------------------------------------------------------------
                                     141
141log⁡(2x2x−11+141−1412x−11+141−112x−11+141)141\frac{\sqrt{141} \log{\left(\frac{2 x}{2 x - 11 + \sqrt{141}} - \frac{\sqrt{141}}{2 x - 11 + \sqrt{141}} - \frac{11}{2 x - 11 + \sqrt{141}} \right)}}{141} 
sqrt(141)*log(-11/(-11 + sqrt(141) + 2*x) - sqrt(141)/(-11 + sqrt(141) + 2*x) + 2*x/(-11 + sqrt(141) + 2*x))/141
Compilar la expresión [src] 
           /         _____     \
  _____    | 2*x - \/ 141  - 11|
\/ 141 *log|-------------------|
           |        _____      |
           \-11 + \/ 141  + 2*x/
--------------------------------
              141
141log⁡((2x−141)−112x+(−11+141))141\frac{\sqrt{141} \log{\left(\frac{\left(2 x - \sqrt{141}\right) - 11}{2 x + \left(-11 + \sqrt{141}\right)} \right)}}{141} 
sqrt(141)*log((2*x - sqrt(141) - 11)/(-11 + sqrt(141) + 2*x))/141
Parte trigonométrica [src] 
           /        _____      \
  _____    |-11 - \/ 141  + 2*x|
\/ 141 *log|-------------------|
           |        _____      |
           \-11 + \/ 141  + 2*x/
--------------------------------
              141
141log⁡(2x−141−112x−11+141)141\frac{\sqrt{141} \log{\left(\frac{2 x - \sqrt{141} - 11}{2 x - 11 + \sqrt{141}} \right)}}{141} 
sqrt(141)*log((-11 - sqrt(141) + 2*x)/(-11 + sqrt(141) + 2*x))/141
Potencias [src] 
           /        _____      \
  _____    |-11 - \/ 141  + 2*x|
\/ 141 *log|-------------------|
           |        _____      |
           \-11 + \/ 141  + 2*x/
--------------------------------
              141
141log⁡(2x−141−112x−11+141)141\frac{\sqrt{141} \log{\left(\frac{2 x - \sqrt{141} - 11}{2 x - 11 + \sqrt{141}} \right)}}{141} 
sqrt(141)*log((-11 - sqrt(141) + 2*x)/(-11 + sqrt(141) + 2*x))/141
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