Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log((8*x-4*sqrt(3))/(4*sqrt(3)+8*x))/(4*sqrt(3))
¿Cómo vas a descomponer esta log((8*x-4*sqrt(3))/(4*sqrt(3)+8*x))/(4*sqrt(3)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ___\
|8*x - 4*\/ 3 |
log|-------------|
| ___ |
\4*\/ 3 + 8*x/
------------------
___
4*\/ 3
$$\frac{\log{\left(\frac{8 x - 4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{4 \sqrt{3}}$$
log((8*x - 4*sqrt(3))/(4*sqrt(3) + 8*x))/((4*sqrt(3)))
Simplificación general
[src]
/ ___ \
___ |- \/ 3 + 2*x|
\/ 3 *log|-------------|
| ___ |
\ \/ 3 + 2*x /
------------------------
12
$$\frac{\sqrt{3} \log{\left(\frac{2 x - \sqrt{3}}{2 x + \sqrt{3}} \right)}}{12}$$
sqrt(3)*log((-sqrt(3) + 2*x)/(sqrt(3) + 2*x))/12
Descomposición de una fracción
[src]
sqrt(3)*log(-4*sqrt(3)/(4*sqrt(3) + 8*x) + 8*x/(4*sqrt(3) + 8*x))/12
$$\frac{\sqrt{3} \log{\left(\frac{8 x}{8 x + 4 \sqrt{3}} - \frac{4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$
/ ___ \
___ | 4*\/ 3 8*x |
\/ 3 *log|- ------------- + -------------|
| ___ ___ |
\ 4*\/ 3 + 8*x 4*\/ 3 + 8*x/
------------------------------------------
12
Respuesta numérica
[src]
0.144337567297406*log((8*x - 4*sqrt(3))/(4*sqrt(3) + 8*x))
0.144337567297406*log((8*x - 4*sqrt(3))/(4*sqrt(3) + 8*x))
Parte trigonométrica
[src]
/ ___ \
___ |- 4*\/ 3 + 8*x|
\/ 3 *log|---------------|
| ___ |
\ 4*\/ 3 + 8*x /
--------------------------
12
$$\frac{\sqrt{3} \log{\left(\frac{8 x - 4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$
sqrt(3)*log((-4*sqrt(3) + 8*x)/(4*sqrt(3) + 8*x))/12
Denominador común
[src]
/ ___ \
___ | \/ 3 2*x |
\/ 3 *log|- ----------- + -----------|
| ___ ___ |
\ \/ 3 + 2*x \/ 3 + 2*x/
--------------------------------------
12
$$\frac{\sqrt{3} \log{\left(\frac{2 x}{2 x + \sqrt{3}} - \frac{\sqrt{3}}{2 x + \sqrt{3}} \right)}}{12}$$
sqrt(3)*log(-sqrt(3)/(sqrt(3) + 2*x) + 2*x/(sqrt(3) + 2*x))/12
Combinatoria
[src]
/ ___ \
___ | 4*\/ 3 8*x |
\/ 3 *log|- ------------- + -------------|
| ___ ___ |
\ 4*\/ 3 + 8*x 4*\/ 3 + 8*x/
------------------------------------------
12
$$\frac{\sqrt{3} \log{\left(\frac{8 x}{8 x + 4 \sqrt{3}} - \frac{4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$
sqrt(3)*log(-4*sqrt(3)/(4*sqrt(3) + 8*x) + 8*x/(4*sqrt(3) + 8*x))/12
Denominador racional
[src]
/ 2 ___\
___ |3 + 4*x - 4*x*\/ 3 |
\/ 3 *log|--------------------|
| 2 |
\ -3 + 4*x /
-------------------------------
12
$$\frac{\sqrt{3} \log{\left(\frac{4 x^{2} - 4 \sqrt{3} x + 3}{4 x^{2} - 3} \right)}}{12}$$
sqrt(3)*log((3 + 4*x^2 - 4*x*sqrt(3))/(-3 + 4*x^2))/12
Unión de expresiones racionales
[src]
/ ___ \
___ |- \/ 3 + 2*x|
\/ 3 *log|-------------|
| ___ |
\ \/ 3 + 2*x /
------------------------
12
$$\frac{\sqrt{3} \log{\left(\frac{2 x - \sqrt{3}}{2 x + \sqrt{3}} \right)}}{12}$$
sqrt(3)*log((-sqrt(3) + 2*x)/(sqrt(3) + 2*x))/12
Potencias
[src]
/ ___ \
___ |- 4*\/ 3 + 8*x|
\/ 3 *log|---------------|
| ___ |
\ 4*\/ 3 + 8*x /
--------------------------
12
$$\frac{\sqrt{3} \log{\left(\frac{8 x - 4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$
sqrt(3)*log((-4*sqrt(3) + 8*x)/(4*sqrt(3) + 8*x))/12
Compilar la expresión
[src]
/ ___\
___ |8*x - 4*\/ 3 |
\/ 3 *log|-------------|
| ___ |
\4*\/ 3 + 8*x/
------------------------
12
$$\frac{\sqrt{3} \log{\left(\frac{8 x - 4 \sqrt{3}}{8 x + 4 \sqrt{3}} \right)}}{12}$$
sqrt(3)*log((8*x - 4*sqrt(3))/(4*sqrt(3) + 8*x))/12