Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(3)/(x*(1-x))+log(3)*log(x)/(1-x)^2
¿Cómo vas a descomponer esta log(3)/(x*(1-x))+log(3)*log(x)/(1-x)^2 expresión en fracciones?
Solución
Ha introducido
[src]
log(3) log(3)*log(x)
--------- + -------------
x*(1 - x) 2
(1 - x)
$$\frac{\log{\left(3 \right)} \log{\left(x \right)}}{\left(1 - x\right)^{2}} + \frac{\log{\left(3 \right)}}{x \left(1 - x\right)}$$
log(3)/((x*(1 - x))) + (log(3)*log(x))/(1 - x)^2
Simplificación general
[src]
(1 - x + x*log(x))*log(3)
-------------------------
2
x*(-1 + x)
$$\frac{\left(x \log{\left(x \right)} - x + 1\right) \log{\left(3 \right)}}{x \left(x - 1\right)^{2}}$$
(1 - x + x*log(x))*log(3)/(x*(-1 + x)^2)
Denominador común
[src]
-x*log(3) + x*log(3)*log(x) + log(3)
------------------------------------
3 2
x + x - 2*x
$$\frac{x \log{\left(3 \right)} \log{\left(x \right)} - x \log{\left(3 \right)} + \log{\left(3 \right)}}{x^{3} - 2 x^{2} + x}$$
(-x*log(3) + x*log(3)*log(x) + log(3))/(x + x^3 - 2*x^2)
Unión de expresiones racionales
[src]
(1 - x + x*log(x))*log(3)
-------------------------
2
x*(1 - x)
$$\frac{\left(x \log{\left(x \right)} - x + 1\right) \log{\left(3 \right)}}{x \left(1 - x\right)^{2}}$$
(1 - x + x*log(x))*log(3)/(x*(1 - x)^2)
Combinatoria
[src]
(1 - x + x*log(x))*log(3)
-------------------------
2
x*(-1 + x)
$$\frac{\left(x \log{\left(x \right)} - x + 1\right) \log{\left(3 \right)}}{x \left(x - 1\right)^{2}}$$
(1 - x + x*log(x))*log(3)/(x*(-1 + x)^2)
Denominador racional
[src]
2
(1 - x) *log(3) + x*(1 - x)*log(3)*log(x)
-----------------------------------------
3
x*(1 - x)
$$\frac{x \left(1 - x\right) \log{\left(3 \right)} \log{\left(x \right)} + \left(1 - x\right)^{2} \log{\left(3 \right)}}{x \left(1 - x\right)^{3}}$$
((1 - x)^2*log(3) + x*(1 - x)*log(3)*log(x))/(x*(1 - x)^3)
Respuesta numérica
[src]
1.09861228866811/(x*(1.0 - x)) + 1.09861228866811*log(x)/(1.0 - x)^2
1.09861228866811/(x*(1.0 - x)) + 1.09861228866811*log(x)/(1.0 - x)^2