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