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Simplificación de expresiones/ Descomposición en fracciones simples/ log((4*x-sqrt(41)-7)/((-7)+sqrt(41)+4*x))/sqrt(41)

¿Cómo vas a descomponer esta log((4*x-sqrt(41)-7)/((-7)+sqrt(41)+4*x))/sqrt(41) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /         ____    \
   | 4*x - \/ 41  - 7|
log|-----------------|
   |       ____      |
   \-7 + \/ 41  + 4*x/
----------------------
          ____        
        \/ 41
log⁡((4x−41)−74x+(−7+41))41\frac{\log{\left(\frac{\left(4 x - \sqrt{41}\right) - 7}{4 x + \left(-7 + \sqrt{41}\right)} \right)}}{\sqrt{41}} 
log((4*x - sqrt(41) - 7)/(-7 + sqrt(41) + 4*x))/sqrt(41)
Descomposición de una fracción [src] 
sqrt(41)*log(-7/(-7 + sqrt(41) + 4*x) - sqrt(41)/(-7 + sqrt(41) + 4*x) + 4*x/(-7 + sqrt(41) + 4*x))/41
41log⁡(4x4x+(−7+41)−74x+(−7+41)−414x+(−7+41))41\frac{\sqrt{41} \log{\left(\frac{4 x}{4 x + \left(-7 + \sqrt{41}\right)} - \frac{7}{4 x + \left(-7 + \sqrt{41}\right)} - \frac{\sqrt{41}}{4 x + \left(-7 + \sqrt{41}\right)} \right)}}{41} 
          /                              ____                         \
  ____    |          7                 \/ 41                4*x       |
\/ 41 *log|- ----------------- - ----------------- + -----------------|
          |         ____                ____                ____      |
          \  -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x/
-----------------------------------------------------------------------
                                   41
Simplificación general [src] 
          /       ____      \
  ____    |-7 - \/ 41  + 4*x|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41
41log⁡(4x−7−414x−7+41)41\frac{\sqrt{41} \log{\left(\frac{4 x - 7 - \sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41} 
sqrt(41)*log((-7 - sqrt(41) + 4*x)/(-7 + sqrt(41) + 4*x))/41
Respuesta numérica [src] 
0.156173761888606*log((4*x - sqrt(41) - 7)/(-7 + sqrt(41) + 4*x))
0.156173761888606*log((4*x - sqrt(41) - 7)/(-7 + sqrt(41) + 4*x))
Unión de expresiones racionales [src] 
          /       ____      \
  ____    |-7 - \/ 41  + 4*x|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41
41log⁡(4x−7−414x−7+41)41\frac{\sqrt{41} \log{\left(\frac{4 x - 7 - \sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41} 
sqrt(41)*log((-7 - sqrt(41) + 4*x)/(-7 + sqrt(41) + 4*x))/41
Denominador común [src] 
          /                              ____                         \
  ____    |          7                 \/ 41                4*x       |
\/ 41 *log|- ----------------- - ----------------- + -----------------|
          |         ____                ____                ____      |
          \  -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x/
-----------------------------------------------------------------------
                                   41
41log⁡(4x4x−7+41−74x−7+41−414x−7+41)41\frac{\sqrt{41} \log{\left(\frac{4 x}{4 x - 7 + \sqrt{41}} - \frac{7}{4 x - 7 + \sqrt{41}} - \frac{\sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41} 
sqrt(41)*log(-7/(-7 + sqrt(41) + 4*x) - sqrt(41)/(-7 + sqrt(41) + 4*x) + 4*x/(-7 + sqrt(41) + 4*x))/41
Combinatoria [src] 
          /                              ____                         \
  ____    |          7                 \/ 41                4*x       |
\/ 41 *log|- ----------------- - ----------------- + -----------------|
          |         ____                ____                ____      |
          \  -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x/
-----------------------------------------------------------------------
                                   41
41log⁡(4x4x−7+41−74x−7+41−414x−7+41)41\frac{\sqrt{41} \log{\left(\frac{4 x}{4 x - 7 + \sqrt{41}} - \frac{7}{4 x - 7 + \sqrt{41}} - \frac{\sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41} 
sqrt(41)*log(-7/(-7 + sqrt(41) + 4*x) - sqrt(41)/(-7 + sqrt(41) + 4*x) + 4*x/(-7 + sqrt(41) + 4*x))/41
Denominador racional [src] 
          / /      ____      \ \
  ____    |-\7 + \/ 41  - 4*x/ |
\/ 41 *log|--------------------|
          |        ____        |
          \ -7 + \/ 41  + 4*x  /
--------------------------------
               41
41log⁡(−−4x+41+74x−7+41)41\frac{\sqrt{41} \log{\left(- \frac{- 4 x + \sqrt{41} + 7}{4 x - 7 + \sqrt{41}} \right)}}{41} 
sqrt(41)*log(-(7 + sqrt(41) - 4*x)/(-7 + sqrt(41) + 4*x))/41
Compilar la expresión [src] 
          /         ____    \
  ____    | 4*x - \/ 41  - 7|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41
41log⁡((4x−41)−74x+(−7+41))41\frac{\sqrt{41} \log{\left(\frac{\left(4 x - \sqrt{41}\right) - 7}{4 x + \left(-7 + \sqrt{41}\right)} \right)}}{41} 
sqrt(41)*log((4*x - sqrt(41) - 7)/(-7 + sqrt(41) + 4*x))/41
Potencias [src] 
          /       ____      \
  ____    |-7 - \/ 41  + 4*x|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41
41log⁡(4x−7−414x−7+41)41\frac{\sqrt{41} \log{\left(\frac{4 x - 7 - \sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41} 
sqrt(41)*log((-7 - sqrt(41) + 4*x)/(-7 + sqrt(41) + 4*x))/41
Parte trigonométrica [src] 
          /       ____      \
  ____    |-7 - \/ 41  + 4*x|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41
41log⁡(4x−7−414x−7+41)41\frac{\sqrt{41} \log{\left(\frac{4 x - 7 - \sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41} 
sqrt(41)*log((-7 - sqrt(41) + 4*x)/(-7 + sqrt(41) + 4*x))/41
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