Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x-3)/(x-3)-exp(x-3)/(x-3)^2
¿Cómo vas a descomponer esta exp(x-3)/(x-3)-exp(x-3)/(x-3)^2 expresión en fracciones?
Solución
Ha introducido
[src]
x - 3 x - 3
e e
------ - --------
x - 3 2
(x - 3)
$$- \frac{e^{x - 3}}{\left(x - 3\right)^{2}} + \frac{e^{x - 3}}{x - 3}$$
exp(x - 3)/(x - 3) - exp(x - 3)/(x - 3)^2
Simplificación general
[src]
/ 2 \ -3 + x
\3 + (-3 + x) - x/*e
---------------------------
3
(-3 + x)
$$\frac{\left(- x + \left(x - 3\right)^{2} + 3\right) e^{x - 3}}{\left(x - 3\right)^{3}}$$
(3 + (-3 + x)^2 - x)*exp(-3 + x)/(-3 + x)^3
Unión de expresiones racionales
[src]
-3 + x
(-4 + x)*e
----------------
2
(-3 + x)
$$\frac{\left(x - 4\right) e^{x - 3}}{\left(x - 3\right)^{2}}$$
(-4 + x)*exp(-3 + x)/(-3 + x)^2
Compilar la expresión
[src]
x - 3 x - 3
e e
------ - ---------
-3 + x 2
(-3 + x)
$$\frac{e^{x - 3}}{x - 3} - \frac{e^{x - 3}}{\left(x - 3\right)^{2}}$$
exp(x - 3)/(-3 + x) - exp(x - 3)/(-3 + x)^2
Combinatoria
[src]
-3 x
(-4 + x)*e *e
---------------
2
(-3 + x)
$$\frac{\left(x - 4\right) e^{x}}{\left(x - 3\right)^{2} e^{3}}$$
(-4 + x)*exp(-3)*exp(x)/(-3 + x)^2
Denominador común
[src]
x x
- 4*e + x*e
---------------------
3 2 3 3
9*e + x *e - 6*x*e
$$\frac{x e^{x} - 4 e^{x}}{x^{2} e^{3} - 6 x e^{3} + 9 e^{3}}$$
(-4*exp(x) + x*exp(x))/(9*exp(3) + x^2*exp(3) - 6*x*exp(3))
Potencias
[src]
-3 + x -3 + x
e e
------- - ---------
-3 + x 2
(-3 + x)
$$\frac{e^{x - 3}}{x - 3} - \frac{e^{x - 3}}{\left(x - 3\right)^{2}}$$
exp(-3 + x)/(-3 + x) - exp(-3 + x)/(-3 + x)^2
Parte trigonométrica
[src]
cosh(-3 + x) + sinh(-3 + x) cosh(-3 + x) + sinh(-3 + x)
--------------------------- - ---------------------------
-3 + x 2
(-3 + x)
$$\frac{\sinh{\left(x - 3 \right)} + \cosh{\left(x - 3 \right)}}{x - 3} - \frac{\sinh{\left(x - 3 \right)} + \cosh{\left(x - 3 \right)}}{\left(x - 3\right)^{2}}$$
-4*cosh(-3 + x) - 4*sinh(-3 + x) + x*cosh(-3 + x) + x*sinh(-3 + x)
------------------------------------------------------------------
2
(-3 + x)
$$\frac{x \sinh{\left(x - 3 \right)} + x \cosh{\left(x - 3 \right)} - 4 \sinh{\left(x - 3 \right)} - 4 \cosh{\left(x - 3 \right)}}{\left(x - 3\right)^{2}}$$
-3 + x -3 + x
e e
------- - ---------
-3 + x 2
(-3 + x)
$$\frac{e^{x - 3}}{x - 3} - \frac{e^{x - 3}}{\left(x - 3\right)^{2}}$$
exp(-3 + x)/(-3 + x) - exp(-3 + x)/(-3 + x)^2
Denominador racional
[src]
-3 + x 2 -3 + x -3 + x
3*e + (-3 + x) *e - x*e
-----------------------------------------
3
(-3 + x)
$$\frac{- x e^{x - 3} + \left(x - 3\right)^{2} e^{x - 3} + 3 e^{x - 3}}{\left(x - 3\right)^{3}}$$
(3*exp(-3 + x) + (-3 + x)^2*exp(-3 + x) - x*exp(-3 + x))/(-3 + x)^3
Respuesta numérica
[src]
exp(x - 3)/(-3.0 + x) - 0.111111111111111*exp(x - 3)/(-1 + 0.333333333333333*x)^2
exp(x - 3)/(-3.0 + x) - 0.111111111111111*exp(x - 3)/(-1 + 0.333333333333333*x)^2