Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log((4-sqrt(2))/(4+sqrt(2)))/(sqrt(2))
¿Cómo vas a descomponer esta log((4-sqrt(2))/(4+sqrt(2)))/(sqrt(2)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ___\
|4 - \/ 2 |
log|---------|
| ___|
\4 + \/ 2 /
--------------
___
\/ 2
$$\frac{\log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{\sqrt{2}}$$
log((4 - sqrt(2))/(4 + sqrt(2)))/sqrt(2)
Simplificación general
[src]
/ ___\ | \/ 2 | | -----| | 2 | |/ ___\ | ||9 4*\/ 2 | | log||- - -------| | \\7 7 / /
$$\log{\left(\left(\frac{9}{7} - \frac{4 \sqrt{2}}{7}\right)^{\frac{\sqrt{2}}{2}} \right)}$$
log((9/7 - 4*sqrt(2)/7)^(sqrt(2)/2))
Denominador común
[src]
___ / ___\ ___ / ___\
\/ 2 *log\4 - \/ 2 / \/ 2 *log\4 + \/ 2 /
-------------------- - --------------------
2 2
$$- \frac{\sqrt{2} \log{\left(\sqrt{2} + 4 \right)}}{2} + \frac{\sqrt{2} \log{\left(4 - \sqrt{2} \right)}}{2}$$
sqrt(2)*log(4 - sqrt(2))/2 - sqrt(2)*log(4 + sqrt(2))/2
Denominador racional
[src]
/ ___\
___ |9 - 4*\/ 2 |
\/ 2 *log|-----------|
\ 7 /
----------------------
2
$$\frac{\sqrt{2} \log{\left(\frac{9 - 4 \sqrt{2}}{7} \right)}}{2}$$
sqrt(2)*log((9 - 4*sqrt(2))/7)/2
Combinatoria
[src]
___ / / ___\ / ___\\
\/ 2 *\- log\4 + \/ 2 / + log\4 - \/ 2 //
-----------------------------------------
2
$$\frac{\sqrt{2} \left(- \log{\left(\sqrt{2} + 4 \right)} + \log{\left(4 - \sqrt{2} \right)}\right)}{2}$$
sqrt(2)*(-log(4 + sqrt(2)) + log(4 - sqrt(2)))/2
Potencias
[src]
/ ___\
___ |4 - \/ 2 |
\/ 2 *log|---------|
| ___|
\4 + \/ 2 /
--------------------
2
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{2}$$
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/2
Unión de expresiones racionales
[src]
/ ___\
___ |4 - \/ 2 |
\/ 2 *log|---------|
| ___|
\4 + \/ 2 /
--------------------
2
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{2}$$
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/2
Parte trigonométrica
[src]
/ ___\
___ |4 - \/ 2 |
\/ 2 *log|---------|
| ___|
\4 + \/ 2 /
--------------------
2
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{2}$$
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/2