Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x)/(x+3)^2+(-6-2*x)*exp(x)/(x+3)^4
¿Cómo vas a descomponer esta exp(x)/(x+3)^2+(-6-2*x)*exp(x)/(x+3)^4 expresión en fracciones?
Solución
Ha introducido
[src]
x x
e (-6 - 2*x)*e
-------- + -------------
2 4
(x + 3) (x + 3)
$$\frac{\left(- 2 x - 6\right) e^{x}}{\left(x + 3\right)^{4}} + \frac{e^{x}}{\left(x + 3\right)^{2}}$$
exp(x)/(x + 3)^2 + ((-6 - 2*x)*exp(x))/(x + 3)^4
Simplificación general
[src]
/ 2 \ x
\-6 + (3 + x) - 2*x/*e
------------------------
4
(3 + x)
$$\frac{\left(- 2 x + \left(x + 3\right)^{2} - 6\right) e^{x}}{\left(x + 3\right)^{4}}$$
(-6 + (3 + x)^2 - 2*x)*exp(x)/(3 + x)^4
Respuesta numérica
[src]
0.111111111111111*exp(x)/(1 + 0.333333333333333*x)^2 + 0.0123456790123457*(-6.0 - 2.0*x)*exp(x)/(1 + 0.333333333333333*x)^4
0.111111111111111*exp(x)/(1 + 0.333333333333333*x)^2 + 0.0123456790123457*(-6.0 - 2.0*x)*exp(x)/(1 + 0.333333333333333*x)^4
Denominador común
[src]
x x
x*e + e
---------------------
3 2
27 + x + 9*x + 27*x
$$\frac{x e^{x} + e^{x}}{x^{3} + 9 x^{2} + 27 x + 27}$$
(x*exp(x) + exp(x))/(27 + x^3 + 9*x^2 + 27*x)
Combinatoria
[src]
x
(1 + x)*e
----------
3
(3 + x)
$$\frac{\left(x + 1\right) e^{x}}{\left(x + 3\right)^{3}}$$
(1 + x)*exp(x)/(3 + x)^3
Denominador racional
[src]
4 x 2 x
(3 + x) *e + (3 + x) *(-6 - 2*x)*e
------------------------------------
6
(3 + x)
$$\frac{\left(- 2 x - 6\right) \left(x + 3\right)^{2} e^{x} + \left(x + 3\right)^{4} e^{x}}{\left(x + 3\right)^{6}}$$
((3 + x)^4*exp(x) + (3 + x)^2*(-6 - 2*x)*exp(x))/(3 + x)^6
Unión de expresiones racionales
[src]
/ 2 \ x
\-6 + (3 + x) - 2*x/*e
------------------------
4
(3 + x)
$$\frac{\left(- 2 x + \left(x + 3\right)^{2} - 6\right) e^{x}}{\left(x + 3\right)^{4}}$$
(-6 + (3 + x)^2 - 2*x)*exp(x)/(3 + x)^4
Parte trigonométrica
[src]
cosh(x) + sinh(x) (-6 - 2*x)*(cosh(x) + sinh(x))
----------------- + ------------------------------
2 4
(3 + x) (3 + x)
$$\frac{\left(- 2 x - 6\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(x + 3\right)^{4}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(x + 3\right)^{2}}$$
x*cosh(x) + x*sinh(x) + cosh(x) + sinh(x)
-----------------------------------------
3
(3 + x)
$$\frac{x \sinh{\left(x \right)} + x \cosh{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(x + 3\right)^{3}}$$
(x*cosh(x) + x*sinh(x) + cosh(x) + sinh(x))/(3 + x)^3