Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x+3)/(x+3)-exp(x+3)/(x+3)^2
¿Cómo vas a descomponer esta exp(x+3)/(x+3)-exp(x+3)/(x+3)^2 expresión en fracciones?
Solución
Ha introducido
[src]
x + 3 x + 3
e e
------ - --------
x + 3 2
(x + 3)
$$- \frac{e^{x + 3}}{\left(x + 3\right)^{2}} + \frac{e^{x + 3}}{x + 3}$$
exp(x + 3)/(x + 3) - exp(x + 3)/(x + 3)^2
Simplificación general
[src]
/ 2 \ 3 + x
\-3 + (3 + x) - x/*e
--------------------------
3
(3 + x)
$$\frac{\left(- x + \left(x + 3\right)^{2} - 3\right) e^{x + 3}}{\left(x + 3\right)^{3}}$$
(-3 + (3 + x)^2 - x)*exp(3 + x)/(3 + x)^3
Denominador común
[src]
3 x 3 x
2*e *e + x*e *e
-----------------
2
9 + x + 6*x
$$\frac{x e^{3} e^{x} + 2 e^{3} e^{x}}{x^{2} + 6 x + 9}$$
(2*exp(3)*exp(x) + x*exp(3)*exp(x))/(9 + x^2 + 6*x)
Combinatoria
[src]
3 x
(2 + x)*e *e
-------------
2
(3 + x)
$$\frac{\left(x + 2\right) e^{3} e^{x}}{\left(x + 3\right)^{2}}$$
(2 + x)*exp(3)*exp(x)/(3 + x)^2
Respuesta numérica
[src]
exp(x + 3)/(3.0 + x) - 0.111111111111111*exp(x + 3)/(1 + 0.333333333333333*x)^2
exp(x + 3)/(3.0 + x) - 0.111111111111111*exp(x + 3)/(1 + 0.333333333333333*x)^2
Denominador racional
[src]
3 + x 2 3 + x 3 + x
- 3*e + (3 + x) *e - x*e
---------------------------------------
3
(3 + x)
$$\frac{- x e^{x + 3} + \left(x + 3\right)^{2} e^{x + 3} - 3 e^{x + 3}}{\left(x + 3\right)^{3}}$$
(-3*exp(3 + x) + (3 + x)^2*exp(3 + x) - x*exp(3 + x))/(3 + x)^3
Unión de expresiones racionales
[src]
3 + x
(2 + x)*e
--------------
2
(3 + x)
$$\frac{\left(x + 2\right) e^{x + 3}}{\left(x + 3\right)^{2}}$$
(2 + x)*exp(3 + x)/(3 + x)^2
Compilar la expresión
[src]
x + 3 x + 3
e e
------ - --------
3 + x 2
(3 + x)
$$\frac{e^{x + 3}}{x + 3} - \frac{e^{x + 3}}{\left(x + 3\right)^{2}}$$
exp(x + 3)/(3 + x) - exp(x + 3)/(3 + x)^2
Parte trigonométrica
[src]
cosh(3 + x) + sinh(3 + x) cosh(3 + x) + sinh(3 + x)
------------------------- - -------------------------
3 + x 2
(3 + x)
$$\frac{\sinh{\left(x + 3 \right)} + \cosh{\left(x + 3 \right)}}{x + 3} - \frac{\sinh{\left(x + 3 \right)} + \cosh{\left(x + 3 \right)}}{\left(x + 3\right)^{2}}$$
2*cosh(3 + x) + 2*sinh(3 + x) + x*cosh(3 + x) + x*sinh(3 + x)
-------------------------------------------------------------
2
(3 + x)
$$\frac{x \sinh{\left(x + 3 \right)} + x \cosh{\left(x + 3 \right)} + 2 \sinh{\left(x + 3 \right)} + 2 \cosh{\left(x + 3 \right)}}{\left(x + 3\right)^{2}}$$
3 + x 3 + x
e e
------ - --------
3 + x 2
(3 + x)
$$\frac{e^{x + 3}}{x + 3} - \frac{e^{x + 3}}{\left(x + 3\right)^{2}}$$
exp(3 + x)/(3 + x) - exp(3 + x)/(3 + x)^2
Potencias
[src]
3 + x 3 + x
e e
------ - --------
3 + x 2
(3 + x)
$$\frac{e^{x + 3}}{x + 3} - \frac{e^{x + 3}}{\left(x + 3\right)^{2}}$$
exp(3 + x)/(3 + x) - exp(3 + x)/(3 + x)^2