Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(x^2-x-1)/2-log((2*x-sqrt(5)-1)/((-1)+sqrt(5)+2*x))/(2*sqrt(5))
¿Cómo vas a descomponer esta log(x^2-x-1)/2-log((2*x-sqrt(5)-1)/((-1)+sqrt(5)+2*x))/(2*sqrt(5)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ___ \
|2*x - \/ 5 - 1 |
log|----------------|
/ 2 \ | ___ |
log\x - x - 1/ \-1 + \/ 5 + 2*x/
--------------- - ---------------------
2 ___
2*\/ 5
$$- \frac{\log{\left(\frac{\left(2 x - \sqrt{5}\right) - 1}{2 x + \left(-1 + \sqrt{5}\right)} \right)}}{2 \sqrt{5}} + \frac{\log{\left(\left(x^{2} - x\right) - 1 \right)}}{2}$$
log(x^2 - x - 1)/2 - log((2*x - sqrt(5) - 1)/(-1 + sqrt(5) + 2*x))/(2*sqrt(5))
Simplificación general
[src]
/ / ___ \ \
___ |-\1 + \/ 5 - 2*x/ |
\/ 5 *log|-------------------|
/ 2 \ | ___ |
log\-1 + x - x/ \ -1 + \/ 5 + 2*x /
---------------- - ------------------------------
2 10
$$- \frac{\sqrt{5} \log{\left(- \frac{- 2 x + 1 + \sqrt{5}}{2 x - 1 + \sqrt{5}} \right)}}{10} + \frac{\log{\left(x^{2} - x - 1 \right)}}{2}$$
log(-1 + x^2 - x)/2 - sqrt(5)*log(-(1 + sqrt(5) - 2*x)/(-1 + sqrt(5) + 2*x))/10
Respuesta numérica
[src]
0.5*log(x^2 - x - 1) - 0.223606797749979*log((2*x - sqrt(5) - 1)/(-1 + sqrt(5) + 2*x))
0.5*log(x^2 - x - 1) - 0.223606797749979*log((2*x - sqrt(5) - 1)/(-1 + sqrt(5) + 2*x))
Potencias
[src]
/ ___ \
___ |-1 - \/ 5 + 2*x|
\/ 5 *log|----------------|
/ 2 \ | ___ |
log\-1 + x - x/ \-1 + \/ 5 + 2*x/
---------------- - ---------------------------
2 10
$$- \frac{\sqrt{5} \log{\left(\frac{2 x - \sqrt{5} - 1}{2 x - 1 + \sqrt{5}} \right)}}{10} + \frac{\log{\left(x^{2} - x - 1 \right)}}{2}$$
log(-1 + x^2 - x)/2 - sqrt(5)*log((-1 - sqrt(5) + 2*x)/(-1 + sqrt(5) + 2*x))/10
Unión de expresiones racionales
[src]
/ ___ \
___ |-1 - \/ 5 + 2*x|
5*log(-1 + x*(-1 + x)) - \/ 5 *log|----------------|
| ___ |
\-1 + \/ 5 + 2*x/
----------------------------------------------------
10
$$\frac{- \sqrt{5} \log{\left(\frac{2 x - \sqrt{5} - 1}{2 x - 1 + \sqrt{5}} \right)} + 5 \log{\left(x \left(x - 1\right) - 1 \right)}}{10}$$
(5*log(-1 + x*(-1 + x)) - sqrt(5)*log((-1 - sqrt(5) + 2*x)/(-1 + sqrt(5) + 2*x)))/10
Combinatoria
[src]
/ ___ \
___ | 1 \/ 5 2*x |
\/ 5 *log|- ---------------- - ---------------- + ----------------|
/ 2 \ | ___ ___ ___ |
log\-1 + x - x/ \ -1 + \/ 5 + 2*x -1 + \/ 5 + 2*x -1 + \/ 5 + 2*x/
---------------- - -------------------------------------------------------------------
2 10
$$\frac{\log{\left(x^{2} - x - 1 \right)}}{2} - \frac{\sqrt{5} \log{\left(\frac{2 x}{2 x - 1 + \sqrt{5}} - \frac{\sqrt{5}}{2 x - 1 + \sqrt{5}} - \frac{1}{2 x - 1 + \sqrt{5}} \right)}}{10}$$
log(-1 + x^2 - x)/2 - sqrt(5)*log(-1/(-1 + sqrt(5) + 2*x) - sqrt(5)/(-1 + sqrt(5) + 2*x) + 2*x/(-1 + sqrt(5) + 2*x))/10
Parte trigonométrica
[src]
/ ___ \
___ |-1 - \/ 5 + 2*x|
\/ 5 *log|----------------|
/ 2 \ | ___ |
log\-1 + x - x/ \-1 + \/ 5 + 2*x/
---------------- - ---------------------------
2 10
$$- \frac{\sqrt{5} \log{\left(\frac{2 x - \sqrt{5} - 1}{2 x - 1 + \sqrt{5}} \right)}}{10} + \frac{\log{\left(x^{2} - x - 1 \right)}}{2}$$
log(-1 + x^2 - x)/2 - sqrt(5)*log((-1 - sqrt(5) + 2*x)/(-1 + sqrt(5) + 2*x))/10
Denominador racional
[src]
/ ___ \
/ 2 \ ___ | 1 \/ 5 2*x |
5*log\-1 + x - x/ - \/ 5 *log|- ---------------- - ---------------- + ----------------|
| ___ ___ ___ |
\ -1 + \/ 5 + 2*x -1 + \/ 5 + 2*x -1 + \/ 5 + 2*x/
----------------------------------------------------------------------------------------
10
$$\frac{5 \log{\left(x^{2} - x - 1 \right)} - \sqrt{5} \log{\left(\frac{2 x}{2 x - 1 + \sqrt{5}} - \frac{\sqrt{5}}{2 x - 1 + \sqrt{5}} - \frac{1}{2 x - 1 + \sqrt{5}} \right)}}{10}$$
(5*log(-1 + x^2 - x) - sqrt(5)*log(-1/(-1 + sqrt(5) + 2*x) - sqrt(5)/(-1 + sqrt(5) + 2*x) + 2*x/(-1 + sqrt(5) + 2*x)))/10
Compilar la expresión
[src]
/ ___ \
___ |2*x - \/ 5 - 1 |
\/ 5 *log|----------------|
/ 2 \ | ___ |
log\x - x - 1/ \-1 + \/ 5 + 2*x/
--------------- - ---------------------------
2 10
$$- \frac{\sqrt{5} \log{\left(\frac{\left(2 x - \sqrt{5}\right) - 1}{2 x + \left(-1 + \sqrt{5}\right)} \right)}}{10} + \frac{\log{\left(\left(x^{2} - x\right) - 1 \right)}}{2}$$
log(x^2 - x - 1)/2 - sqrt(5)*log((2*x - sqrt(5) - 1)/(-1 + sqrt(5) + 2*x))/10
Denominador común
[src]
/ ___ \
___ | 1 \/ 5 2*x |
\/ 5 *log|- ---------------- - ---------------- + ----------------|
/ 2 \ | ___ ___ ___ |
log\-1 + x - x/ \ -1 + \/ 5 + 2*x -1 + \/ 5 + 2*x -1 + \/ 5 + 2*x/
---------------- - -------------------------------------------------------------------
2 10
$$\frac{\log{\left(x^{2} - x - 1 \right)}}{2} - \frac{\sqrt{5} \log{\left(\frac{2 x}{2 x - 1 + \sqrt{5}} - \frac{\sqrt{5}}{2 x - 1 + \sqrt{5}} - \frac{1}{2 x - 1 + \sqrt{5}} \right)}}{10}$$
log(-1 + x^2 - x)/2 - sqrt(5)*log(-1/(-1 + sqrt(5) + 2*x) - sqrt(5)/(-1 + sqrt(5) + 2*x) + 2*x/(-1 + sqrt(5) + 2*x))/10