Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x)/(e^x+2)-(e^x+4)*exp(x)/(e^x+2)^2
¿Cómo vas a descomponer esta exp(x)/(e^x+2)-(e^x+4)*exp(x)/(e^x+2)^2 expresión en fracciones?
Solución
Ha introducido
[src]
x / x \ x
e \E + 4/*e
------ - -----------
x 2
E + 2 / x \
\E + 2/
$$- \frac{\left(e^{x} + 4\right) e^{x}}{\left(e^{x} + 2\right)^{2}} + \frac{e^{x}}{e^{x} + 2}$$
exp(x)/(E^x + 2) - (E^x + 4)*exp(x)/(E^x + 2)^2
Simplificación general
[src]
x
-2*e
---------
2
/ x\
\2 + e /
$$- \frac{2 e^{x}}{\left(e^{x} + 2\right)^{2}}$$
-2*exp(x)/(2 + exp(x))^2
Descomposición de una fracción
[src]
-2/(2 + exp(x)) + 4/(2 + exp(x))^2
$$- \frac{2}{e^{x} + 2} + \frac{4}{\left(e^{x} + 2\right)^{2}}$$
2 4
- ------ + ---------
x 2
2 + e / x\
\2 + e /
Respuesta numérica
[src]
exp(x)/(2.0 + 2.71828182845905^x) - 0.25*(4.0 + 2.71828182845905^x)*exp(x)/(1 + 0.5*2.71828182845905^x)^2
exp(x)/(2.0 + 2.71828182845905^x) - 0.25*(4.0 + 2.71828182845905^x)*exp(x)/(1 + 0.5*2.71828182845905^x)^2
Unión de expresiones racionales
[src]
x
-2*e
---------
2
/ x\
\2 + e /
$$- \frac{2 e^{x}}{\left(e^{x} + 2\right)^{2}}$$
-2*exp(x)/(2 + exp(x))^2
Potencias
[src]
x / x\ x
e \-4 - e /*e
------ + ------------
x 2
2 + e / x\
\2 + e /
$$\frac{\left(- e^{x} - 4\right) e^{x}}{\left(e^{x} + 2\right)^{2}} + \frac{e^{x}}{e^{x} + 2}$$
x / x\ x
e \4 + e /*e
------ - -----------
x 2
2 + e / x\
\2 + e /
$$\frac{e^{x}}{e^{x} + 2} - \frac{\left(e^{x} + 4\right) e^{x}}{\left(e^{x} + 2\right)^{2}}$$
exp(x)/(2 + exp(x)) - (4 + exp(x))*exp(x)/(2 + exp(x))^2
Denominador racional
[src]
2
/ x\ x / x\ / x\ x
\2 + e / *e - \2 + e /*\4 + e /*e
-----------------------------------
3
/ x\
\2 + e /
$$\frac{\left(e^{x} + 2\right)^{2} e^{x} - \left(e^{x} + 2\right) \left(e^{x} + 4\right) e^{x}}{\left(e^{x} + 2\right)^{3}}$$
((2 + exp(x))^2*exp(x) - (2 + exp(x))*(4 + exp(x))*exp(x))/(2 + exp(x))^3
Denominador común
[src]
x
-2*e
---------------
x 2*x
4 + 4*e + e
$$- \frac{2 e^{x}}{e^{2 x} + 4 e^{x} + 4}$$
-2*exp(x)/(4 + 4*exp(x) + exp(2*x))
Compilar la expresión
[src]
x / x\ x
e \4 + e /*e
------ - -----------
x 2
2 + e / x\
\2 + e /
$$\frac{e^{x}}{e^{x} + 2} - \frac{\left(e^{x} + 4\right) e^{x}}{\left(e^{x} + 2\right)^{2}}$$
exp(x)/(2 + exp(x)) - (4 + exp(x))*exp(x)/(2 + exp(x))^2
Combinatoria
[src]
x
-2*e
---------
2
/ x\
\2 + e /
$$- \frac{2 e^{x}}{\left(e^{x} + 2\right)^{2}}$$
-2*exp(x)/(2 + exp(x))^2
Parte trigonométrica
[src]
cosh(x) + sinh(x) (cosh(x) + sinh(x))*(4 + cosh(x) + sinh(x))
--------------------- - -------------------------------------------
2 + cosh(x) + sinh(x) 2
(2 + cosh(x) + sinh(x))
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sinh{\left(x \right)} + \cosh{\left(x \right)} + 2} - \frac{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)} + 4\right)}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} + 2\right)^{2}}$$
-2*(cosh(x) + sinh(x))
---------------------------
2
/ x\
\2 + (cosh(1) + sinh(1)) /
$$- \frac{2 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 2\right)^{2}}$$
/ x\
cosh(x) + sinh(x) \4 + (cosh(1) + sinh(1)) /*(cosh(x) + sinh(x))
------------------------ - ----------------------------------------------
x 2
2 + (cosh(1) + sinh(1)) / x\
\2 + (cosh(1) + sinh(1)) /
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 2} - \frac{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 4\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 2\right)^{2}}$$
-2*(cosh(x) + sinh(x))
------------------------
2
(2 + cosh(x) + sinh(x))
$$- \frac{2 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} + 2\right)^{2}}$$
x / x\ x
e \4 + e /*e
------ - -----------
x 2
2 + e / x\
\2 + e /
$$\frac{e^{x}}{e^{x} + 2} - \frac{\left(e^{x} + 4\right) e^{x}}{\left(e^{x} + 2\right)^{2}}$$
exp(x)/(2 + exp(x)) - (4 + exp(x))*exp(x)/(2 + exp(x))^2