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