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