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
$$- \frac{\sqrt{5} \log{\left(\frac{2 x - \sqrt{5} + 1}{2 x + 1 + \sqrt{5}} \right)}}{10} + \frac{\log{\left(x^{2} + x - 1 \right)}}{2}$$
log(-1 + x + x^2)/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))
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
$$\frac{5 \log{\left(x^{2} + x - 1 \right)} - \sqrt{5} \log{\left(\frac{2 x}{2 x + \left(1 + \sqrt{5}\right)} - \frac{\sqrt{5}}{2 x + \left(1 + \sqrt{5}\right)} + \frac{1}{2 x + \left(1 + \sqrt{5}\right)} \right)}}{10}$$
(5*log(-1 + x + 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
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 + x^2)/2 - sqrt(5)*log((1 - sqrt(5) + 2*x)/(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 + x^2)/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
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
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 + x^2)/2 - 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 + x^2)/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
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