Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(x-5*x^2)/(2*sqrt(x+2))+sqrt(x+2)*(1-10*x)/(x-5*x^2)
¿Cómo vas a descomponer esta log(x-5*x^2)/(2*sqrt(x+2))+sqrt(x+2)*(1-10*x)/(x-5*x^2) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2\ _______
log\x - 5*x / \/ x + 2 *(1 - 10*x)
------------- + --------------------
_______ 2
2*\/ x + 2 x - 5*x
$$\frac{\left(1 - 10 x\right) \sqrt{x + 2}}{- 5 x^{2} + x} + \frac{\log{\left(- 5 x^{2} + x \right)}}{2 \sqrt{x + 2}}$$
log(x - 5*x^2)/((2*sqrt(x + 2))) + (sqrt(x + 2)*(1 - 10*x))/(x - 5*x^2)
Simplificación general
[src]
x*(-1 + 5*x)*log(x*(1 - 5*x))
(-1 + 10*x)*(2 + x) + -----------------------------
2
---------------------------------------------------
_______
x*(-1 + 5*x)*\/ 2 + x
$$\frac{\frac{x \left(5 x - 1\right) \log{\left(x \left(1 - 5 x\right) \right)}}{2} + \left(x + 2\right) \left(10 x - 1\right)}{x \sqrt{x + 2} \left(5 x - 1\right)}$$
((-1 + 10*x)*(2 + x) + x*(-1 + 5*x)*log(x*(1 - 5*x))/2)/(x*(-1 + 5*x)*sqrt(2 + x))
Denominador racional
[src]
2 / 2\ 2 / 2\
-4 + 20*x + 38*x - x*log\x - 5*x / + 5*x *log\x - 5*x /
--------------------------------------------------------
_______ / 2\
2*\/ 2 + x *\-x + 5*x /
$$\frac{5 x^{2} \log{\left(- 5 x^{2} + x \right)} + 20 x^{2} - x \log{\left(- 5 x^{2} + x \right)} + 38 x - 4}{2 \sqrt{x + 2} \left(5 x^{2} - x\right)}$$
(-4 + 20*x^2 + 38*x - x*log(x - 5*x^2) + 5*x^2*log(x - 5*x^2))/(2*sqrt(2 + x)*(-x + 5*x^2))
Respuesta numérica
[src]
0.353553390593274*(1 + 0.5*x)^(-0.5)*log(x - 5*x^2) + 1.4142135623731*(1 + 0.5*x)^0.5*(1.0 - 10.0*x)/(x - 5.0*x^2)
0.353553390593274*(1 + 0.5*x)^(-0.5)*log(x - 5*x^2) + 1.4142135623731*(1 + 0.5*x)^0.5*(1.0 - 10.0*x)/(x - 5.0*x^2)
Combinatoria
[src]
2 / 2\ 2 / 2\
-4 + 20*x + 38*x - x*log\x - 5*x / + 5*x *log\x - 5*x /
--------------------------------------------------------
_______
2*x*(-1 + 5*x)*\/ 2 + x
$$\frac{5 x^{2} \log{\left(- 5 x^{2} + x \right)} + 20 x^{2} - x \log{\left(- 5 x^{2} + x \right)} + 38 x - 4}{2 x \sqrt{x + 2} \left(5 x - 1\right)}$$
(-4 + 20*x^2 + 38*x - x*log(x - 5*x^2) + 5*x^2*log(x - 5*x^2))/(2*x*(-1 + 5*x)*sqrt(2 + x))
Denominador común
[src]
2 / 2\ 2 / 2\
-4 + 20*x + 38*x - x*log\x - 5*x / + 5*x *log\x - 5*x /
--------------------------------------------------------
_______ 2 _______
- 2*x*\/ 2 + x + 10*x *\/ 2 + x
$$\frac{5 x^{2} \log{\left(- 5 x^{2} + x \right)} + 20 x^{2} - x \log{\left(- 5 x^{2} + x \right)} + 38 x - 4}{10 x^{2} \sqrt{x + 2} - 2 x \sqrt{x + 2}}$$
(-4 + 20*x^2 + 38*x - x*log(x - 5*x^2) + 5*x^2*log(x - 5*x^2))/(-2*x*sqrt(2 + x) + 10*x^2*sqrt(2 + x))
Unión de expresiones racionales
[src]
2*(1 - 10*x)*(2 + x) + x*(1 - 5*x)*log(x*(1 - 5*x))
---------------------------------------------------
_______
2*x*(1 - 5*x)*\/ 2 + x
$$\frac{x \left(1 - 5 x\right) \log{\left(x \left(1 - 5 x\right) \right)} + 2 \left(1 - 10 x\right) \left(x + 2\right)}{2 x \left(1 - 5 x\right) \sqrt{x + 2}}$$
(2*(1 - 10*x)*(2 + x) + x*(1 - 5*x)*log(x*(1 - 5*x)))/(2*x*(1 - 5*x)*sqrt(2 + x))