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Simplificación de expresiones/
Descomposición en fracciones simples/
log((2*x-sqrt(5)+7)/(7+sqrt(5)+2*x))/sqrt(5)
¿Cómo vas a descomponer esta log((2*x-sqrt(5)+7)/(7+sqrt(5)+2*x))/sqrt(5) expresión en fracciones?
Solución
Ha introducido
[src]
/ ___ \
|2*x - \/ 5 + 7|
log|---------------|
| ___ |
\7 + \/ 5 + 2*x/
--------------------
___
\/ 5
$$\frac{\log{\left(\frac{\left(2 x - \sqrt{5}\right) + 7}{2 x + \left(\sqrt{5} + 7\right)} \right)}}{\sqrt{5}}$$
log((2*x - sqrt(5) + 7)/(7 + sqrt(5) + 2*x))/sqrt(5)
Descomposición de una fracción
[src]
sqrt(5)*log(7/(7 + sqrt(5) + 2*x) - sqrt(5)/(7 + sqrt(5) + 2*x) + 2*x/(7 + sqrt(5) + 2*x))/5
$$\frac{\sqrt{5} \log{\left(\frac{2 x}{2 x + \left(\sqrt{5} + 7\right)} - \frac{\sqrt{5}}{2 x + \left(\sqrt{5} + 7\right)} + \frac{7}{2 x + \left(\sqrt{5} + 7\right)} \right)}}{5}$$
/ ___ \
___ | 7 \/ 5 2*x |
\/ 5 *log|--------------- - --------------- + ---------------|
| ___ ___ ___ |
\7 + \/ 5 + 2*x 7 + \/ 5 + 2*x 7 + \/ 5 + 2*x/
--------------------------------------------------------------
5
Simplificación general
[src]
/ ___ \
___ |7 - \/ 5 + 2*x|
\/ 5 *log|---------------|
| ___ |
\7 + \/ 5 + 2*x/
--------------------------
5
$$\frac{\sqrt{5} \log{\left(\frac{2 x - \sqrt{5} + 7}{2 x + \sqrt{5} + 7} \right)}}{5}$$
sqrt(5)*log((7 - sqrt(5) + 2*x)/(7 + sqrt(5) + 2*x))/5
Respuesta numérica
[src]
0.447213595499958*log((2*x - sqrt(5) + 7)/(7 + sqrt(5) + 2*x))
0.447213595499958*log((2*x - sqrt(5) + 7)/(7 + sqrt(5) + 2*x))
Parte trigonométrica
[src]
/ ___ \
___ |7 - \/ 5 + 2*x|
\/ 5 *log|---------------|
| ___ |
\7 + \/ 5 + 2*x/
--------------------------
5
$$\frac{\sqrt{5} \log{\left(\frac{2 x - \sqrt{5} + 7}{2 x + \sqrt{5} + 7} \right)}}{5}$$
sqrt(5)*log((7 - sqrt(5) + 2*x)/(7 + sqrt(5) + 2*x))/5
Unión de expresiones racionales
[src]
/ ___ \
___ |7 - \/ 5 + 2*x|
\/ 5 *log|---------------|
| ___ |
\7 + \/ 5 + 2*x/
--------------------------
5
$$\frac{\sqrt{5} \log{\left(\frac{2 x - \sqrt{5} + 7}{2 x + \sqrt{5} + 7} \right)}}{5}$$
sqrt(5)*log((7 - sqrt(5) + 2*x)/(7 + sqrt(5) + 2*x))/5
Potencias
[src]
/ ___ \
___ |7 - \/ 5 + 2*x|
\/ 5 *log|---------------|
| ___ |
\7 + \/ 5 + 2*x/
--------------------------
5
$$\frac{\sqrt{5} \log{\left(\frac{2 x - \sqrt{5} + 7}{2 x + \sqrt{5} + 7} \right)}}{5}$$
sqrt(5)*log((7 - sqrt(5) + 2*x)/(7 + sqrt(5) + 2*x))/5
Denominador común
[src]
/ ___ \
___ | 7 \/ 5 2*x |
\/ 5 *log|--------------- - --------------- + ---------------|
| ___ ___ ___ |
\7 + \/ 5 + 2*x 7 + \/ 5 + 2*x 7 + \/ 5 + 2*x/
--------------------------------------------------------------
5
$$\frac{\sqrt{5} \log{\left(\frac{2 x}{2 x + \sqrt{5} + 7} - \frac{\sqrt{5}}{2 x + \sqrt{5} + 7} + \frac{7}{2 x + \sqrt{5} + 7} \right)}}{5}$$
sqrt(5)*log(7/(7 + sqrt(5) + 2*x) - sqrt(5)/(7 + sqrt(5) + 2*x) + 2*x/(7 + sqrt(5) + 2*x))/5
Combinatoria
[src]
/ ___ \
___ | 7 \/ 5 2*x |
\/ 5 *log|--------------- - --------------- + ---------------|
| ___ ___ ___ |
\7 + \/ 5 + 2*x 7 + \/ 5 + 2*x 7 + \/ 5 + 2*x/
--------------------------------------------------------------
5
$$\frac{\sqrt{5} \log{\left(\frac{2 x}{2 x + \sqrt{5} + 7} - \frac{\sqrt{5}}{2 x + \sqrt{5} + 7} + \frac{7}{2 x + \sqrt{5} + 7} \right)}}{5}$$
sqrt(5)*log(7/(7 + sqrt(5) + 2*x) - sqrt(5)/(7 + sqrt(5) + 2*x) + 2*x/(7 + sqrt(5) + 2*x))/5
Denominador racional
[src]
/ ___ \
___ |7 - \/ 5 + 2*x|
\/ 5 *log|---------------|
| ___ |
\7 + \/ 5 + 2*x/
--------------------------
5
$$\frac{\sqrt{5} \log{\left(\frac{2 x - \sqrt{5} + 7}{2 x + \left(\sqrt{5} + 7\right)} \right)}}{5}$$
sqrt(5)*log((7 - sqrt(5) + 2*x)/(7 + sqrt(5) + 2*x))/5
Compilar la expresión
[src]
/ ___ \
___ |2*x - \/ 5 + 7|
\/ 5 *log|---------------|
| ___ |
\7 + \/ 5 + 2*x/
--------------------------
5
$$\frac{\sqrt{5} \log{\left(\frac{\left(2 x - \sqrt{5}\right) + 7}{2 x + \left(\sqrt{5} + 7\right)} \right)}}{5}$$
sqrt(5)*log((2*x - sqrt(5) + 7)/(7 + sqrt(5) + 2*x))/5