Sr Examen

Otras calculadoras

¿Cómo vas a descomponer esta log(x^2+5*x-2)/2-(5*log((2*x-sqrt(33)+5)/(2*x+sqrt(33)+5)))/(2*sqrt(33)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
                         /        ____    \
                         |2*x - \/ 33  + 5|
                    5*log|----------------|
   / 2          \        |        ____    |
log\x  + 5*x - 2/        \2*x + \/ 33  + 5/
----------------- - -----------------------
        2                       ____       
                            2*\/ 33        
$$- \frac{5 \log{\left(\frac{\left(2 x - \sqrt{33}\right) + 5}{\left(2 x + \sqrt{33}\right) + 5} \right)}}{2 \sqrt{33}} + \frac{\log{\left(\left(x^{2} + 5 x\right) - 2 \right)}}{2}$$
log(x^2 + 5*x - 2)/2 - 5*log((2*x - sqrt(33) + 5)/(2*x + sqrt(33) + 5))/(2*sqrt(33))
Simplificación general [src]
                                 /      ____      \
                         ____    |5 - \/ 33  + 2*x|
                     5*\/ 33 *log|----------------|
   /      2      \               |      ____      |
log\-2 + x  + 5*x/               \5 + \/ 33  + 2*x/
------------------ - ------------------------------
        2                          66              
$$- \frac{5 \sqrt{33} \log{\left(\frac{2 x - \sqrt{33} + 5}{2 x + 5 + \sqrt{33}} \right)}}{66} + \frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log((5 - sqrt(33) + 2*x)/(5 + sqrt(33) + 2*x))/66
Potencias [src]
                                 /      ____      \
                         ____    |5 - \/ 33  + 2*x|
                     5*\/ 33 *log|----------------|
   /      2      \               |      ____      |
log\-2 + x  + 5*x/               \5 + \/ 33  + 2*x/
------------------ - ------------------------------
        2                          66              
$$- \frac{5 \sqrt{33} \log{\left(\frac{2 x - \sqrt{33} + 5}{2 x + 5 + \sqrt{33}} \right)}}{66} + \frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log((5 - sqrt(33) + 2*x)/(5 + sqrt(33) + 2*x))/66
Parte trigonométrica [src]
                                 /      ____      \
                         ____    |5 - \/ 33  + 2*x|
                     5*\/ 33 *log|----------------|
   /      2      \               |      ____      |
log\-2 + x  + 5*x/               \5 + \/ 33  + 2*x/
------------------ - ------------------------------
        2                          66              
$$- \frac{5 \sqrt{33} \log{\left(\frac{2 x - \sqrt{33} + 5}{2 x + 5 + \sqrt{33}} \right)}}{66} + \frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log((5 - sqrt(33) + 2*x)/(5 + sqrt(33) + 2*x))/66
Denominador racional [src]
                                    /                          ____                        \
      /      2      \       ____    |       5                \/ 33               2*x       |
33*log\-2 + x  + 5*x/ - 5*\/ 33 *log|---------------- - ---------------- + ----------------|
                                    |        ____               ____               ____    |
                                    \2*x + \/ 33  + 5   2*x + \/ 33  + 5   2*x + \/ 33  + 5/
--------------------------------------------------------------------------------------------
                                             66                                             
$$\frac{33 \log{\left(x^{2} + 5 x - 2 \right)} - 5 \sqrt{33} \log{\left(\frac{2 x}{\left(2 x + \sqrt{33}\right) + 5} - \frac{\sqrt{33}}{\left(2 x + \sqrt{33}\right) + 5} + \frac{5}{\left(2 x + \sqrt{33}\right) + 5} \right)}}{66}$$
(33*log(-2 + x^2 + 5*x) - 5*sqrt(33)*log(5/(2*x + sqrt(33) + 5) - sqrt(33)/(2*x + sqrt(33) + 5) + 2*x/(2*x + sqrt(33) + 5)))/66
Denominador común [src]
                                 /                          ____                        \
                         ____    |       5                \/ 33               2*x       |
                     5*\/ 33 *log|---------------- - ---------------- + ----------------|
   /      2      \               |      ____               ____               ____      |
log\-2 + x  + 5*x/               \5 + \/ 33  + 2*x   5 + \/ 33  + 2*x   5 + \/ 33  + 2*x/
------------------ - --------------------------------------------------------------------
        2                                             66                                 
$$\frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2} - \frac{5 \sqrt{33} \log{\left(\frac{2 x}{2 x + 5 + \sqrt{33}} - \frac{\sqrt{33}}{2 x + 5 + \sqrt{33}} + \frac{5}{2 x + 5 + \sqrt{33}} \right)}}{66}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log(5/(5 + sqrt(33) + 2*x) - sqrt(33)/(5 + sqrt(33) + 2*x) + 2*x/(5 + sqrt(33) + 2*x))/66
Compilar la expresión [src]
                                /        ____    \
                        ____    |2*x - \/ 33  + 5|
                    5*\/ 33 *log|----------------|
   / 2          \               |        ____    |
log\x  + 5*x - 2/               \2*x + \/ 33  + 5/
----------------- - ------------------------------
        2                         66              
$$- \frac{5 \sqrt{33} \log{\left(\frac{\left(2 x - \sqrt{33}\right) + 5}{\left(2 x + \sqrt{33}\right) + 5} \right)}}{66} + \frac{\log{\left(\left(x^{2} + 5 x\right) - 2 \right)}}{2}$$
log(x^2 + 5*x - 2)/2 - 5*sqrt(33)*log((2*x - sqrt(33) + 5)/(2*x + sqrt(33) + 5))/66
Abrimos la expresión [src]
                                /        ____    \
                        ____    |2*x - \/ 33  + 5|
                    5*\/ 33 *log|----------------|
   / 2          \               |        ____    |
log\x  + 5*x - 2/               \2*x + \/ 33  + 5/
----------------- - ------------------------------
        2                         66              
$$- \frac{5 \sqrt{33} \log{\left(\frac{\left(2 x - \sqrt{33}\right) + 5}{\left(2 x + \sqrt{33}\right) + 5} \right)}}{66} + \frac{\log{\left(\left(x^{2} + 5 x\right) - 2 \right)}}{2}$$
log(x^2 + 5*x - 2)/2 - 5*sqrt(33)*log((2*x - sqrt(33) + 5)/(2*x + sqrt(33) + 5))/66
Respuesta numérica [src]
0.5*log(x^2 + 5*x - 2) - 0.435194139889245*log((2*x - sqrt(33) + 5)/(2*x + sqrt(33) + 5))
0.5*log(x^2 + 5*x - 2) - 0.435194139889245*log((2*x - sqrt(33) + 5)/(2*x + sqrt(33) + 5))
Unión de expresiones racionales [src]
                                     /      ____      \
                             ____    |5 - \/ 33  + 2*x|
33*log(-2 + x*(5 + x)) - 5*\/ 33 *log|----------------|
                                     |      ____      |
                                     \5 + \/ 33  + 2*x/
-------------------------------------------------------
                           66                          
$$\frac{- 5 \sqrt{33} \log{\left(\frac{2 x - \sqrt{33} + 5}{2 x + 5 + \sqrt{33}} \right)} + 33 \log{\left(x \left(x + 5\right) - 2 \right)}}{66}$$
(33*log(-2 + x*(5 + x)) - 5*sqrt(33)*log((5 - sqrt(33) + 2*x)/(5 + sqrt(33) + 2*x)))/66
Combinatoria [src]
                                 /                          ____                        \
                         ____    |       5                \/ 33               2*x       |
                     5*\/ 33 *log|---------------- - ---------------- + ----------------|
   /      2      \               |      ____               ____               ____      |
log\-2 + x  + 5*x/               \5 + \/ 33  + 2*x   5 + \/ 33  + 2*x   5 + \/ 33  + 2*x/
------------------ - --------------------------------------------------------------------
        2                                             66                                 
$$\frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2} - \frac{5 \sqrt{33} \log{\left(\frac{2 x}{2 x + 5 + \sqrt{33}} - \frac{\sqrt{33}}{2 x + 5 + \sqrt{33}} + \frac{5}{2 x + 5 + \sqrt{33}} \right)}}{66}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log(5/(5 + sqrt(33) + 2*x) - sqrt(33)/(5 + sqrt(33) + 2*x) + 2*x/(5 + sqrt(33) + 2*x))/66