Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log((4-sqrt(2))/(4+sqrt(2)))/(4*sqrt(2))
¿Cómo vas a descomponer esta log((4-sqrt(2))/(4+sqrt(2)))/(4*sqrt(2)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ___\
|4 - \/ 2 |
log|---------|
| ___|
\4 + \/ 2 /
--------------
___
4*\/ 2
$$\frac{\log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{4 \sqrt{2}}$$
log((4 - sqrt(2))/(4 + sqrt(2)))/((4*sqrt(2)))
Simplificación general
[src]
/ ___\ | \/ 2 | | -----| | 8 | |/ ___\ | ||9 4*\/ 2 | | log||- - -------| | \\7 7 / /
$$\log{\left(\left(\frac{9}{7} - \frac{4 \sqrt{2}}{7}\right)^{\frac{\sqrt{2}}{8}} \right)}$$
log((9/7 - 4*sqrt(2)/7)^(sqrt(2)/8))
Parte trigonométrica
[src]
/ ___\
___ |4 - \/ 2 |
\/ 2 *log|---------|
| ___|
\4 + \/ 2 /
--------------------
8
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{8}$$
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/8
Combinatoria
[src]
___ / / ___\ / ___\\
\/ 2 *\- log\4 + \/ 2 / + log\4 - \/ 2 //
-----------------------------------------
8
$$\frac{\sqrt{2} \left(- \log{\left(\sqrt{2} + 4 \right)} + \log{\left(4 - \sqrt{2} \right)}\right)}{8}$$
sqrt(2)*(-log(4 + sqrt(2)) + log(4 - sqrt(2)))/8
Unión de expresiones racionales
[src]
/ ___\
___ |4 - \/ 2 |
\/ 2 *log|---------|
| ___|
\4 + \/ 2 /
--------------------
8
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{8}$$
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/8
Denominador común
[src]
___ / ___\ ___ / ___\
\/ 2 *log\4 + \/ 2 / \/ 2 *log\4 - \/ 2 /
- -------------------- + --------------------
8 8
$$- \frac{\sqrt{2} \log{\left(\sqrt{2} + 4 \right)}}{8} + \frac{\sqrt{2} \log{\left(4 - \sqrt{2} \right)}}{8}$$
-sqrt(2)*log(4 + sqrt(2))/8 + sqrt(2)*log(4 - sqrt(2))/8
Denominador racional
[src]
/ ___\
___ |9 - 4*\/ 2 |
\/ 2 *log|-----------|
\ 7 /
----------------------
8
$$\frac{\sqrt{2} \log{\left(\frac{9 - 4 \sqrt{2}}{7} \right)}}{8}$$
sqrt(2)*log((9 - 4*sqrt(2))/7)/8
Potencias
[src]
/ ___\
___ |4 - \/ 2 |
\/ 2 *log|---------|
| ___|
\4 + \/ 2 /
--------------------
8
$$\frac{\sqrt{2} \log{\left(\frac{4 - \sqrt{2}}{\sqrt{2} + 4} \right)}}{8}$$
sqrt(2)*log((4 - sqrt(2))/(4 + sqrt(2)))/8