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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2+4*x-7)/2-log((2*x-2*sqrt(11)+4)/(4+2*sqrt(11)+2*x))/sqrt(11)

¿Cómo vas a descomponer esta log(x^2+4*x-7)/2-log((2*x-2*sqrt(11)+4)/(4+2*sqrt(11)+2*x))/sqrt(11) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                       /          ____    \
                       |2*x - 2*\/ 11  + 4|
                    log|------------------|
   / 2          \      |        ____      |
log\x  + 4*x - 7/      \4 + 2*\/ 11  + 2*x/
----------------- - -----------------------
        2                      ____        
                             \/ 11
−log⁡((2x−211)+42x+(4+211))11+log⁡((x2+4x)−7)2- \frac{\log{\left(\frac{\left(2 x - 2 \sqrt{11}\right) + 4}{2 x + \left(4 + 2 \sqrt{11}\right)} \right)}}{\sqrt{11}} + \frac{\log{\left(\left(x^{2} + 4 x\right) - 7 \right)}}{2} 
log(x^2 + 4*x - 7)/2 - log((2*x - 2*sqrt(11) + 4)/(4 + 2*sqrt(11) + 2*x))/sqrt(11)
Simplificación general [src] 
                               /          ____\
                       ____    |2 + x - \/ 11 |
                     \/ 11 *log|--------------|
   /      2      \             |          ____|
log\-7 + x  + 4*x/             \2 + x + \/ 11 /
------------------ - --------------------------
        2                        11
−11log⁡(x−11+2x+2+11)11+log⁡(x2+4x−7)2- \frac{\sqrt{11} \log{\left(\frac{x - \sqrt{11} + 2}{x + 2 + \sqrt{11}} \right)}}{11} + \frac{\log{\left(x^{2} + 4 x - 7 \right)}}{2} 
log(-7 + x^2 + 4*x)/2 - sqrt(11)*log((2 + x - sqrt(11))/(2 + x + sqrt(11)))/11
Respuesta numérica [src] 
0.5*log(x^2 + 4*x - 7) - 0.301511344577764*log((2*x - 2*sqrt(11) + 4)/(4 + 2*sqrt(11) + 2*x))
0.5*log(x^2 + 4*x - 7) - 0.301511344577764*log((2*x - 2*sqrt(11) + 4)/(4 + 2*sqrt(11) + 2*x))
Parte trigonométrica [src] 
                               /        ____      \
                       ____    |4 - 2*\/ 11  + 2*x|
                     \/ 11 *log|------------------|
   /      2      \             |              ____|
log\-7 + x  + 4*x/             \4 + 2*x + 2*\/ 11 /
------------------ - ------------------------------
        2                          11
−11log⁡(2x−211+42x+4+211)11+log⁡(x2+4x−7)2- \frac{\sqrt{11} \log{\left(\frac{2 x - 2 \sqrt{11} + 4}{2 x + 4 + 2 \sqrt{11}} \right)}}{11} + \frac{\log{\left(x^{2} + 4 x - 7 \right)}}{2} 
log(-7 + x^2 + 4*x)/2 - sqrt(11)*log((4 - 2*sqrt(11) + 2*x)/(4 + 2*x + 2*sqrt(11)))/11
Denominador racional [src] 
                                    /                              ____                          \
      /      2      \       ____    |        4                 2*\/ 11                2*x        |
11*log\-7 + x  + 4*x/ - 2*\/ 11 *log|------------------ - ------------------ + ------------------|
                                    |        ____                 ____                 ____      |
                                    \4 + 2*\/ 11  + 2*x   4 + 2*\/ 11  + 2*x   4 + 2*\/ 11  + 2*x/
--------------------------------------------------------------------------------------------------
                                                22
11log⁡(x2+4x−7)−211log⁡(2x2x+(4+211)−2112x+(4+211)+42x+(4+211))22\frac{11 \log{\left(x^{2} + 4 x - 7 \right)} - 2 \sqrt{11} \log{\left(\frac{2 x}{2 x + \left(4 + 2 \sqrt{11}\right)} - \frac{2 \sqrt{11}}{2 x + \left(4 + 2 \sqrt{11}\right)} + \frac{4}{2 x + \left(4 + 2 \sqrt{11}\right)} \right)}}{22} 
(11*log(-7 + x^2 + 4*x) - 2*sqrt(11)*log(4/(4 + 2*sqrt(11) + 2*x) - 2*sqrt(11)/(4 + 2*sqrt(11) + 2*x) + 2*x/(4 + 2*sqrt(11) + 2*x)))/22
Denominador común [src] 
                               /                                        ____    \
                       ____    |      2                x              \/ 11     |
                     \/ 11 *log|-------------- + -------------- - --------------|
   /      2      \             |          ____             ____             ____|
log\-7 + x  + 4*x/             \2 + x + \/ 11    2 + x + \/ 11    2 + x + \/ 11 /
------------------ - ------------------------------------------------------------
        2                                         11
log⁡(x2+4x−7)2−11log⁡(xx+2+11−11x+2+11+2x+2+11)11\frac{\log{\left(x^{2} + 4 x - 7 \right)}}{2} - \frac{\sqrt{11} \log{\left(\frac{x}{x + 2 + \sqrt{11}} - \frac{\sqrt{11}}{x + 2 + \sqrt{11}} + \frac{2}{x + 2 + \sqrt{11}} \right)}}{11} 
log(-7 + x^2 + 4*x)/2 - sqrt(11)*log(2/(2 + x + sqrt(11)) + x/(2 + x + sqrt(11)) - sqrt(11)/(2 + x + sqrt(11)))/11
Potencias [src] 
                               /        ____      \
                       ____    |4 - 2*\/ 11  + 2*x|
                     \/ 11 *log|------------------|
   /      2      \             |              ____|
log\-7 + x  + 4*x/             \4 + 2*x + 2*\/ 11 /
------------------ - ------------------------------
        2                          11
−11log⁡(2x−211+42x+4+211)11+log⁡(x2+4x−7)2- \frac{\sqrt{11} \log{\left(\frac{2 x - 2 \sqrt{11} + 4}{2 x + 4 + 2 \sqrt{11}} \right)}}{11} + \frac{\log{\left(x^{2} + 4 x - 7 \right)}}{2} 
log(-7 + x^2 + 4*x)/2 - sqrt(11)*log((4 - 2*sqrt(11) + 2*x)/(4 + 2*x + 2*sqrt(11)))/11
Combinatoria [src] 
                               /                              ____                          \
                       ____    |        4                 2*\/ 11                2*x        |
                     \/ 11 *log|------------------ - ------------------ + ------------------|
   /      2      \             |              ____                 ____                 ____|
log\-7 + x  + 4*x/             \4 + 2*x + 2*\/ 11    4 + 2*x + 2*\/ 11    4 + 2*x + 2*\/ 11 /
------------------ - ------------------------------------------------------------------------
        2                                               11
log⁡(x2+4x−7)2−11log⁡(2x2x+4+211−2112x+4+211+42x+4+211)11\frac{\log{\left(x^{2} + 4 x - 7 \right)}}{2} - \frac{\sqrt{11} \log{\left(\frac{2 x}{2 x + 4 + 2 \sqrt{11}} - \frac{2 \sqrt{11}}{2 x + 4 + 2 \sqrt{11}} + \frac{4}{2 x + 4 + 2 \sqrt{11}} \right)}}{11} 
log(-7 + x^2 + 4*x)/2 - sqrt(11)*log(4/(4 + 2*x + 2*sqrt(11)) - 2*sqrt(11)/(4 + 2*x + 2*sqrt(11)) + 2*x/(4 + 2*x + 2*sqrt(11)))/11
Unión de expresiones racionales [src] 
                                     /          ____\
                             ____    |2 + x - \/ 11 |
11*log(-7 + x*(4 + x)) - 2*\/ 11 *log|--------------|
                                     |          ____|
                                     \2 + x + \/ 11 /
-----------------------------------------------------
                          22
−211log⁡(x−11+2x+2+11)+11log⁡(x(x+4)−7)22\frac{- 2 \sqrt{11} \log{\left(\frac{x - \sqrt{11} + 2}{x + 2 + \sqrt{11}} \right)} + 11 \log{\left(x \left(x + 4\right) - 7 \right)}}{22} 
(11*log(-7 + x*(4 + x)) - 2*sqrt(11)*log((2 + x - sqrt(11))/(2 + x + sqrt(11))))/22
Compilar la expresión [src] 
                              /          ____    \
                      ____    |2*x - 2*\/ 11  + 4|
                    \/ 11 *log|------------------|
   / 2          \             |        ____      |
log\x  + 4*x - 7/             \4 + 2*\/ 11  + 2*x/
----------------- - ------------------------------
        2                         11
−11log⁡((2x−211)+42x+(4+211))11+log⁡((x2+4x)−7)2- \frac{\sqrt{11} \log{\left(\frac{\left(2 x - 2 \sqrt{11}\right) + 4}{2 x + \left(4 + 2 \sqrt{11}\right)} \right)}}{11} + \frac{\log{\left(\left(x^{2} + 4 x\right) - 7 \right)}}{2} 
log(x^2 + 4*x - 7)/2 - sqrt(11)*log((2*x - 2*sqrt(11) + 4)/(4 + 2*sqrt(11) + 2*x))/11
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