Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x)/(2*x-1)-2*exp(x)/(2*x-1)^2
¿Cómo vas a descomponer esta exp(x)/(2*x-1)-2*exp(x)/(2*x-1)^2 expresión en fracciones?
Solución
Ha introducido
[src]
x x
e 2*e
------- - ----------
2*x - 1 2
(2*x - 1)
$$- \frac{2 e^{x}}{\left(2 x - 1\right)^{2}} + \frac{e^{x}}{2 x - 1}$$
exp(x)/(2*x - 1) - 2*exp(x)/(2*x - 1)^2
Simplificación general
[src]
x
(-3 + 2*x)*e
--------------
2
1 - 4*x + 4*x
$$\frac{\left(2 x - 3\right) e^{x}}{4 x^{2} - 4 x + 1}$$
(-3 + 2*x)*exp(x)/(1 - 4*x + 4*x^2)
Respuesta numérica
[src]
exp(x)/(-1.0 + 2.0*x) - 0.5*exp(x)/(-0.5 + x)^2
exp(x)/(-1.0 + 2.0*x) - 0.5*exp(x)/(-0.5 + x)^2
Compilar la expresión
[src]
x x
e 2*e
-------- - -----------
-1 + 2*x 2
(-1 + 2*x)
$$\frac{e^{x}}{2 x - 1} - \frac{2 e^{x}}{\left(2 x - 1\right)^{2}}$$
exp(x)/(-1 + 2*x) - 2*exp(x)/(-1 + 2*x)^2
Denominador común
[src]
x x
- 3*e + 2*x*e
---------------
2
1 - 4*x + 4*x
$$\frac{2 x e^{x} - 3 e^{x}}{4 x^{2} - 4 x + 1}$$
(-3*exp(x) + 2*x*exp(x))/(1 - 4*x + 4*x^2)
Combinatoria
[src]
x
(-3 + 2*x)*e
-------------
2
(-1 + 2*x)
$$\frac{\left(2 x - 3\right) e^{x}}{\left(2 x - 1\right)^{2}}$$
(-3 + 2*x)*exp(x)/(-1 + 2*x)^2
Potencias
[src]
x x
e 2*e
-------- - -----------
-1 + 2*x 2
(-1 + 2*x)
$$\frac{e^{x}}{2 x - 1} - \frac{2 e^{x}}{\left(2 x - 1\right)^{2}}$$
exp(x)/(-1 + 2*x) - 2*exp(x)/(-1 + 2*x)^2
Denominador racional
[src]
2 x x
(-1 + 2*x) *e - 2*(-1 + 2*x)*e
--------------------------------
3
(-1 + 2*x)
$$\frac{\left(2 x - 1\right)^{2} e^{x} - 2 \left(2 x - 1\right) e^{x}}{\left(2 x - 1\right)^{3}}$$
((-1 + 2*x)^2*exp(x) - 2*(-1 + 2*x)*exp(x))/(-1 + 2*x)^3
Unión de expresiones racionales
[src]
x
(-3 + 2*x)*e
-------------
2
(-1 + 2*x)
$$\frac{\left(2 x - 3\right) e^{x}}{\left(2 x - 1\right)^{2}}$$
(-3 + 2*x)*exp(x)/(-1 + 2*x)^2
Parte trigonométrica
[src]
cosh(x) + sinh(x) 2*cosh(x) + 2*sinh(x)
----------------- - ---------------------
-1 + 2*x 2
(-1 + 2*x)
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{2 x - 1} - \frac{2 \sinh{\left(x \right)} + 2 \cosh{\left(x \right)}}{\left(2 x - 1\right)^{2}}$$
cosh(x) + sinh(x) 2*(cosh(x) + sinh(x))
----------------- - ---------------------
-1 + 2*x 2
(-1 + 2*x)
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{2 x - 1} - \frac{2 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(2 x - 1\right)^{2}}$$
x x
e 2*e
-------- - -----------
-1 + 2*x 2
(-1 + 2*x)
$$\frac{e^{x}}{2 x - 1} - \frac{2 e^{x}}{\left(2 x - 1\right)^{2}}$$
exp(x)/(-1 + 2*x) - 2*exp(x)/(-1 + 2*x)^2