Sr Examen
¿Cómo vas a descomponer esta exp(x)/(x+5)-(1+E^x)/(x+5)^2 expresión en fracciones?
Solución
Ha introducido
[src]
x x
e 1 + E
----- - --------
x + 5 2
(x + 5)
$$- \frac{e^{x} + 1}{\left(x + 5\right)^{2}} + \frac{e^{x}}{x + 5}$$
exp(x)/(x + 5) - (1 + E^x)/(x + 5)^2
Simplificación general
[src]
x x
-1 - e + (5 + x)*e
--------------------
2
(5 + x)
$$\frac{\left(x + 5\right) e^{x} - e^{x} - 1}{\left(x + 5\right)^{2}}$$
(-1 - exp(x) + (5 + x)*exp(x))/(5 + x)^2
Respuesta numérica
[src]
exp(x)/(5.0 + x) - 0.04*(1.0 + 2.71828182845905^x)/(1 + 0.2*x)^2
exp(x)/(5.0 + x) - 0.04*(1.0 + 2.71828182845905^x)/(1 + 0.2*x)^2
Compilar la expresión
[src]
x x
e 1 + e
----- - --------
5 + x 2
(5 + x)
$$\frac{e^{x}}{x + 5} - \frac{e^{x} + 1}{\left(x + 5\right)^{2}}$$
exp(x)/(5 + x) - (1 + exp(x))/(5 + x)^2
Denominador racional
[src]
2 x / x\
(5 + x) *e + \-1 - e /*(5 + x)
-------------------------------
3
(5 + x)
$$\frac{\left(x + 5\right)^{2} e^{x} + \left(x + 5\right) \left(- e^{x} - 1\right)}{\left(x + 5\right)^{3}}$$
((5 + x)^2*exp(x) + (-1 - exp(x))*(5 + x))/(5 + x)^3
Denominador común
[src]
x x
-1 + 4*e + x*e
----------------
2
25 + x + 10*x
$$\frac{x e^{x} + 4 e^{x} - 1}{x^{2} + 10 x + 25}$$
(-1 + 4*exp(x) + x*exp(x))/(25 + x^2 + 10*x)
Potencias
[src]
x x
e -1 - e
----- + --------
5 + x 2
(5 + x)
$$\frac{e^{x}}{x + 5} + \frac{- e^{x} - 1}{\left(x + 5\right)^{2}}$$
x x
e 1 + e
----- - --------
5 + x 2
(5 + x)
$$\frac{e^{x}}{x + 5} - \frac{e^{x} + 1}{\left(x + 5\right)^{2}}$$
exp(x)/(5 + x) - (1 + exp(x))/(5 + x)^2
Unión de expresiones racionales
[src]
x x
-1 - e + (5 + x)*e
--------------------
2
(5 + x)
$$\frac{\left(x + 5\right) e^{x} - e^{x} - 1}{\left(x + 5\right)^{2}}$$
(-1 - exp(x) + (5 + x)*exp(x))/(5 + x)^2
Combinatoria
[src]
x x
-1 + 4*e + x*e
----------------
2
(5 + x)
$$\frac{x e^{x} + 4 e^{x} - 1}{\left(x + 5\right)^{2}}$$
(-1 + 4*exp(x) + x*exp(x))/(5 + x)^2
Parte trigonométrica
[src]
cosh(x) + sinh(x) 1 + cosh(x) + sinh(x)
----------------- - ---------------------
5 + x 2
(5 + x)
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{x + 5} - \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)} + 1}{\left(x + 5\right)^{2}}$$
x x
e 1 + e
----- - --------
5 + x 2
(5 + x)
$$\frac{e^{x}}{x + 5} - \frac{e^{x} + 1}{\left(x + 5\right)^{2}}$$
x
cosh(x) + sinh(x) 1 + (cosh(1) + sinh(1))
----------------- - ------------------------
5 + x 2
(5 + x)
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{x + 5} - \frac{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 1}{\left(x + 5\right)^{2}}$$
(cosh(x) + sinh(x))/(5 + x) - (1 + (cosh(1) + sinh(1))^x)/(5 + x)^2