Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x)/(e^x-e^3)-exp(2*x)/(e^x-e^3)^2
¿Cómo vas a descomponer esta exp(x)/(e^x-e^3)-exp(2*x)/(e^x-e^3)^2 expresión en fracciones?
Solución
Ha introducido
[src]
x 2*x
e e
------- - ----------
x 3 2
E - E / x 3\
\E - E /
$$- \frac{e^{2 x}}{\left(e^{x} - e^{3}\right)^{2}} + \frac{e^{x}}{e^{x} - e^{3}}$$
exp(x)/(E^x - E^3) - exp(2*x)/(E^x - E^3)^2
Simplificación general
[src]
3 + x
-e
----------------------
3 + x 6 2*x
- 2*e + e + e
$$- \frac{e^{x + 3}}{e^{2 x} - 2 e^{x + 3} + e^{6}}$$
-exp(3 + x)/(-2*exp(3 + x) + exp(6) + exp(2*x))
Respuesta numérica
[src]
exp(x)/(-20.0855369231877 + 2.71828182845905^x) - 0.00247875217666636*exp(2*x)/(-1 + 0.049787068367864*2.71828182845905^x)^2
exp(x)/(-20.0855369231877 + 2.71828182845905^x) - 0.00247875217666636*exp(2*x)/(-1 + 0.049787068367864*2.71828182845905^x)^2
Denominador racional
[src]
2
/ 3 x\ x / 3 x\ 2*x
\- e + e / *e - \- e + e /*e
----------------------------------
3
/ 3 x\
\- e + e /
$$\frac{\left(e^{x} - e^{3}\right)^{2} e^{x} - \left(e^{x} - e^{3}\right) e^{2 x}}{\left(e^{x} - e^{3}\right)^{3}}$$
((-exp(3) + exp(x))^2*exp(x) - (-exp(3) + exp(x))*exp(2*x))/(-exp(3) + exp(x))^3
Compilar la expresión
[src]
x 2*x
e e
--------- - ------------
3 x 2
- e + e / 3 x\
\- e + e /
$$\frac{e^{x}}{e^{x} - e^{3}} - \frac{e^{2 x}}{\left(e^{x} - e^{3}\right)^{2}}$$
exp(x)/(-exp(3) + exp(x)) - exp(2*x)/(-exp(3) + exp(x))^2
Unión de expresiones racionales
[src]
3 x
-e *e
------------
2
/ 3 x\
\- e + e /
$$- \frac{e^{3} e^{x}}{\left(e^{x} - e^{3}\right)^{2}}$$
-exp(3)*exp(x)/(-exp(3) + exp(x))^2
Combinatoria
[src]
3 x
-e *e
------------
2
/ x 3\
\- e + e /
$$- \frac{e^{3} e^{x}}{\left(- e^{x} + e^{3}\right)^{2}}$$
-exp(3)*exp(x)/(-exp(x) + exp(3))^2
Potencias
[src]
x 2*x
e e
--------- - ------------
3 x 2
- e + e / 3 x\
\- e + e /
$$\frac{e^{x}}{e^{x} - e^{3}} - \frac{e^{2 x}}{\left(e^{x} - e^{3}\right)^{2}}$$
exp(x)/(-exp(3) + exp(x)) - exp(2*x)/(-exp(3) + exp(x))^2
Denominador común
[src]
3 x
-e *e
---------------------
3 x 6 2*x
- 2*e *e + e + e
$$- \frac{e^{3} e^{x}}{e^{2 x} - 2 e^{3} e^{x} + e^{6}}$$
-exp(3)*exp(x)/(-2*exp(3)*exp(x) + exp(6) + exp(2*x))
Parte trigonométrica
[src]
-(cosh(3 + x) + sinh(3 + x))
-----------------------------------------
2
(-cosh(3) - sinh(3) + cosh(x) + sinh(x))
$$- \frac{\sinh{\left(x + 3 \right)} + \cosh{\left(x + 3 \right)}}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} - \cosh{\left(3 \right)} - \sinh{\left(3 \right)}\right)^{2}}$$
cosh(x) + sinh(x) cosh(2*x) + sinh(2*x)
------------------------------------------- - ----------------------------------------------
x 3 2
(cosh(1) + sinh(1)) - (cosh(1) + sinh(1)) / x 3\
\(cosh(1) + sinh(1)) - (cosh(1) + sinh(1)) /
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} - \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{3}} - \frac{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} - \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{3}\right)^{2}}$$
cosh(x) + sinh(x) cosh(2*x) + sinh(2*x)
-------------------------------------- - -----------------------------------------
-cosh(3) - sinh(3) + cosh(x) + sinh(x) 2
(-cosh(3) - sinh(3) + cosh(x) + sinh(x))
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sinh{\left(x \right)} + \cosh{\left(x \right)} - \cosh{\left(3 \right)} - \sinh{\left(3 \right)}} - \frac{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} - \cosh{\left(3 \right)} - \sinh{\left(3 \right)}\right)^{2}}$$
x 2*x
e e
--------- - ------------
3 x 2
- e + e / 3 x\
\- e + e /
$$\frac{e^{x}}{e^{x} - e^{3}} - \frac{e^{2 x}}{\left(e^{x} - e^{3}\right)^{2}}$$
exp(x)/(-exp(3) + exp(x)) - exp(2*x)/(-exp(3) + exp(x))^2