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Simplificación de expresiones/ Descomposición en fracciones simples/ log((6*x-2*sqrt(22)+8)/(8+2*sqrt(22)+6*x))/(2*sqrt(22))

¿Cómo vas a descomponer esta log((6*x-2*sqrt(22)+8)/(8+2*sqrt(22)+6*x))/(2*sqrt(22)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ____    \
   |6*x - 2*\/ 22  + 8|
log|------------------|
   |        ____      |
   \8 + 2*\/ 22  + 6*x/
-----------------------
            ____       
        2*\/ 22
log⁡((6x−222)+86x+(8+222))222\frac{\log{\left(\frac{\left(6 x - 2 \sqrt{22}\right) + 8}{6 x + \left(8 + 2 \sqrt{22}\right)} \right)}}{2 \sqrt{22}} 
log((6*x - 2*sqrt(22) + 8)/(8 + 2*sqrt(22) + 6*x))/((2*sqrt(22)))
Descomposición de una fracción [src] 
sqrt(22)*log(8/(8 + 2*sqrt(22) + 6*x) - 2*sqrt(22)/(8 + 2*sqrt(22) + 6*x) + 6*x/(8 + 2*sqrt(22) + 6*x))/44
22log⁡(6x6x+(8+222)−2226x+(8+222)+86x+(8+222))44\frac{\sqrt{22} \log{\left(\frac{6 x}{6 x + \left(8 + 2 \sqrt{22}\right)} - \frac{2 \sqrt{22}}{6 x + \left(8 + 2 \sqrt{22}\right)} + \frac{8}{6 x + \left(8 + 2 \sqrt{22}\right)} \right)}}{44} 
          /                              ____                          \
  ____    |        8                 2*\/ 22                6*x        |
\/ 22 *log|------------------ - ------------------ + ------------------|
          |        ____                 ____                 ____      |
          \8 + 2*\/ 22  + 6*x   8 + 2*\/ 22  + 6*x   8 + 2*\/ 22  + 6*x/
------------------------------------------------------------------------
                                   44
Simplificación general [src] 
          /      ____      \
  ____    |4 - \/ 22  + 3*x|
\/ 22 *log|----------------|
          |      ____      |
          \4 + \/ 22  + 3*x/
----------------------------
             44
22log⁡(3x−22+43x+4+22)44\frac{\sqrt{22} \log{\left(\frac{3 x - \sqrt{22} + 4}{3 x + 4 + \sqrt{22}} \right)}}{44} 
sqrt(22)*log((4 - sqrt(22) + 3*x)/(4 + sqrt(22) + 3*x))/44
Respuesta numérica [src] 
0.106600358177805*log((6*x - 2*sqrt(22) + 8)/(8 + 2*sqrt(22) + 6*x))
0.106600358177805*log((6*x - 2*sqrt(22) + 8)/(8 + 2*sqrt(22) + 6*x))
Potencias [src] 
          /        ____      \
  ____    |8 - 2*\/ 22  + 6*x|
\/ 22 *log|------------------|
          |        ____      |
          \8 + 2*\/ 22  + 6*x/
------------------------------
              44
22log⁡(6x−222+86x+8+222)44\frac{\sqrt{22} \log{\left(\frac{6 x - 2 \sqrt{22} + 8}{6 x + 8 + 2 \sqrt{22}} \right)}}{44} 
sqrt(22)*log((8 - 2*sqrt(22) + 6*x)/(8 + 2*sqrt(22) + 6*x))/44
Combinatoria [src] 
          /                              ____                          \
  ____    |        8                 2*\/ 22                6*x        |
\/ 22 *log|------------------ - ------------------ + ------------------|
          |        ____                 ____                 ____      |
          \8 + 2*\/ 22  + 6*x   8 + 2*\/ 22  + 6*x   8 + 2*\/ 22  + 6*x/
------------------------------------------------------------------------
                                   44
22log⁡(6x6x+8+222−2226x+8+222+86x+8+222)44\frac{\sqrt{22} \log{\left(\frac{6 x}{6 x + 8 + 2 \sqrt{22}} - \frac{2 \sqrt{22}}{6 x + 8 + 2 \sqrt{22}} + \frac{8}{6 x + 8 + 2 \sqrt{22}} \right)}}{44} 
sqrt(22)*log(8/(8 + 2*sqrt(22) + 6*x) - 2*sqrt(22)/(8 + 2*sqrt(22) + 6*x) + 6*x/(8 + 2*sqrt(22) + 6*x))/44
Unión de expresiones racionales [src] 
          /      ____      \
  ____    |4 - \/ 22  + 3*x|
\/ 22 *log|----------------|
          |      ____      |
          \4 + \/ 22  + 3*x/
----------------------------
             44
22log⁡(3x−22+43x+4+22)44\frac{\sqrt{22} \log{\left(\frac{3 x - \sqrt{22} + 4}{3 x + 4 + \sqrt{22}} \right)}}{44} 
sqrt(22)*log((4 - sqrt(22) + 3*x)/(4 + sqrt(22) + 3*x))/44
Denominador común [src] 
          /                          ____                        \
  ____    |       4                \/ 22               3*x       |
\/ 22 *log|---------------- - ---------------- + ----------------|
          |      ____               ____               ____      |
          \4 + \/ 22  + 3*x   4 + \/ 22  + 3*x   4 + \/ 22  + 3*x/
------------------------------------------------------------------
                                44
22log⁡(3x3x+4+22−223x+4+22+43x+4+22)44\frac{\sqrt{22} \log{\left(\frac{3 x}{3 x + 4 + \sqrt{22}} - \frac{\sqrt{22}}{3 x + 4 + \sqrt{22}} + \frac{4}{3 x + 4 + \sqrt{22}} \right)}}{44} 
sqrt(22)*log(4/(4 + sqrt(22) + 3*x) - sqrt(22)/(4 + sqrt(22) + 3*x) + 3*x/(4 + sqrt(22) + 3*x))/44
Denominador racional [src] 
          /  /      ____      \\
  ____    |2*\4 - \/ 22  + 3*x/|
\/ 22 *log|--------------------|
          |         ____       |
          \ 8 + 2*\/ 22  + 6*x /
--------------------------------
               44
22log⁡(2(3x−22+4)6x+(8+222))44\frac{\sqrt{22} \log{\left(\frac{2 \left(3 x - \sqrt{22} + 4\right)}{6 x + \left(8 + 2 \sqrt{22}\right)} \right)}}{44} 
sqrt(22)*log(2*(4 - sqrt(22) + 3*x)/(8 + 2*sqrt(22) + 6*x))/44
Parte trigonométrica [src] 
          /        ____      \
  ____    |8 - 2*\/ 22  + 6*x|
\/ 22 *log|------------------|
          |        ____      |
          \8 + 2*\/ 22  + 6*x/
------------------------------
              44
22log⁡(6x−222+86x+8+222)44\frac{\sqrt{22} \log{\left(\frac{6 x - 2 \sqrt{22} + 8}{6 x + 8 + 2 \sqrt{22}} \right)}}{44} 
sqrt(22)*log((8 - 2*sqrt(22) + 6*x)/(8 + 2*sqrt(22) + 6*x))/44
Abrimos la expresión [src] 
          /          ____    \
  ____    |6*x - 2*\/ 22  + 8|
\/ 22 *log|------------------|
          |        ____      |
          \8 + 2*\/ 22  + 6*x/
------------------------------
              44
22log⁡((6x−222)+86x+(8+222))44\frac{\sqrt{22} \log{\left(\frac{\left(6 x - 2 \sqrt{22}\right) + 8}{6 x + \left(8 + 2 \sqrt{22}\right)} \right)}}{44} 
sqrt(22)*log((6*x - 2*sqrt(22) + 8)/(8 + 2*sqrt(22) + 6*x))/44
Compilar la expresión [src] 
          /          ____    \
  ____    |6*x - 2*\/ 22  + 8|
\/ 22 *log|------------------|
          |        ____      |
          \8 + 2*\/ 22  + 6*x/
------------------------------
              44
22log⁡((6x−222)+86x+(8+222))44\frac{\sqrt{22} \log{\left(\frac{\left(6 x - 2 \sqrt{22}\right) + 8}{6 x + \left(8 + 2 \sqrt{22}\right)} \right)}}{44} 
sqrt(22)*log((6*x - 2*sqrt(22) + 8)/(8 + 2*sqrt(22) + 6*x))/44
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