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Simplificación de expresiones/ Descomposición en fracciones simples/ log((6*x-2*sqrt(21))/(2*sqrt(21)+6*x))/(2*sqrt(21))

¿Cómo vas a descomponer esta log((6*x-2*sqrt(21))/(2*sqrt(21)+6*x))/(2*sqrt(21)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /          ____\
   |6*x - 2*\/ 21 |
log|--------------|
   |    ____      |
   \2*\/ 21  + 6*x/
-------------------
          ____     
      2*\/ 21
log⁡(6x−2216x+221)221\frac{\log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{2 \sqrt{21}} 
log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))/((2*sqrt(21)))
Descomposición de una fracción [src] 
sqrt(21)*log(-2*sqrt(21)/(2*sqrt(21) + 6*x) + 6*x/(2*sqrt(21) + 6*x))/42
21log⁡(6x6x+221−2216x+221)42\frac{\sqrt{21} \log{\left(\frac{6 x}{6 x + 2 \sqrt{21}} - \frac{2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42} 
          /         ____                    \
  ____    |     2*\/ 21            6*x      |
\/ 21 *log|- -------------- + --------------|
          |      ____             ____      |
          \  2*\/ 21  + 6*x   2*\/ 21  + 6*x/
---------------------------------------------
                      42
Simplificación general [src] 
          /    ____      \
  ____    |- \/ 21  + 3*x|
\/ 21 *log|--------------|
          |   ____       |
          \ \/ 21  + 3*x /
--------------------------
            42
21log⁡(3x−213x+21)42\frac{\sqrt{21} \log{\left(\frac{3 x - \sqrt{21}}{3 x + \sqrt{21}} \right)}}{42} 
sqrt(21)*log((-sqrt(21) + 3*x)/(sqrt(21) + 3*x))/42
Potencias [src] 
          /      ____      \
  ____    |- 2*\/ 21  + 6*x|
\/ 21 *log|----------------|
          |     ____       |
          \ 2*\/ 21  + 6*x /
----------------------------
             42
21log⁡(6x−2216x+221)42\frac{\sqrt{21} \log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42} 
sqrt(21)*log((-2*sqrt(21) + 6*x)/(2*sqrt(21) + 6*x))/42
Parte trigonométrica [src] 
          /      ____      \
  ____    |- 2*\/ 21  + 6*x|
\/ 21 *log|----------------|
          |     ____       |
          \ 2*\/ 21  + 6*x /
----------------------------
             42
21log⁡(6x−2216x+221)42\frac{\sqrt{21} \log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42} 
sqrt(21)*log((-2*sqrt(21) + 6*x)/(2*sqrt(21) + 6*x))/42
Denominador racional [src] 
          /       2         ____\
  ____    |7 + 3*x  - 2*x*\/ 21 |
\/ 21 *log|---------------------|
          |              2      |
          \      -7 + 3*x       /
---------------------------------
                42
21log⁡(3x2−221x+73x2−7)42\frac{\sqrt{21} \log{\left(\frac{3 x^{2} - 2 \sqrt{21} x + 7}{3 x^{2} - 7} \right)}}{42} 
sqrt(21)*log((7 + 3*x^2 - 2*x*sqrt(21))/(-7 + 3*x^2))/42
Combinatoria [src] 
          /         ____                    \
  ____    |     2*\/ 21            6*x      |
\/ 21 *log|- -------------- + --------------|
          |      ____             ____      |
          \  2*\/ 21  + 6*x   2*\/ 21  + 6*x/
---------------------------------------------
                      42
21log⁡(6x6x+221−2216x+221)42\frac{\sqrt{21} \log{\left(\frac{6 x}{6 x + 2 \sqrt{21}} - \frac{2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42} 
sqrt(21)*log(-2*sqrt(21)/(2*sqrt(21) + 6*x) + 6*x/(2*sqrt(21) + 6*x))/42
Unión de expresiones racionales [src] 
          /    ____      \
  ____    |- \/ 21  + 3*x|
\/ 21 *log|--------------|
          |   ____       |
          \ \/ 21  + 3*x /
--------------------------
            42
21log⁡(3x−213x+21)42\frac{\sqrt{21} \log{\left(\frac{3 x - \sqrt{21}}{3 x + \sqrt{21}} \right)}}{42} 
sqrt(21)*log((-sqrt(21) + 3*x)/(sqrt(21) + 3*x))/42
Denominador común [src] 
          /       ____                  \
  ____    |     \/ 21           3*x     |
\/ 21 *log|- ------------ + ------------|
          |    ____           ____      |
          \  \/ 21  + 3*x   \/ 21  + 3*x/
-----------------------------------------
                    42
21log⁡(3x3x+21−213x+21)42\frac{\sqrt{21} \log{\left(\frac{3 x}{3 x + \sqrt{21}} - \frac{\sqrt{21}}{3 x + \sqrt{21}} \right)}}{42} 
sqrt(21)*log(-sqrt(21)/(sqrt(21) + 3*x) + 3*x/(sqrt(21) + 3*x))/42
Abrimos la expresión [src] 
          /          ____\
  ____    |6*x - 2*\/ 21 |
\/ 21 *log|--------------|
          |    ____      |
          \2*\/ 21  + 6*x/
--------------------------
            42
21log⁡(6x−2216x+221)42\frac{\sqrt{21} \log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42} 
sqrt(21)*log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))/42
Compilar la expresión [src] 
          /          ____\
  ____    |6*x - 2*\/ 21 |
\/ 21 *log|--------------|
          |    ____      |
          \2*\/ 21  + 6*x/
--------------------------
            42
21log⁡(6x−2216x+221)42\frac{\sqrt{21} \log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42} 
sqrt(21)*log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))/42
Respuesta numérica [src] 
0.109108945117996*log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))
0.109108945117996*log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))
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