Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
-exp(-6-3*x)/(x+2)^2-3*exp(-6-3*x)/(x+2)
¿Cómo vas a descomponer esta -exp(-6-3*x)/(x+2)^2-3*exp(-6-3*x)/(x+2) expresión en fracciones?
Solución
Ha introducido
[src]
-6 - 3*x -6 - 3*x
-e 3*e
----------- - -----------
2 x + 2
(x + 2)
$$\frac{\left(-1\right) e^{- 3 x - 6}}{\left(x + 2\right)^{2}} - \frac{3 e^{- 3 x - 6}}{x + 2}$$
(-exp(-6 - 3*x))/(x + 2)^2 - 3*exp(-6 - 3*x)/(x + 2)
Simplificación general
[src]
-6 - 3*x
-(7 + 3*x)*e
---------------------
2
4 + x + 4*x
$$- \frac{\left(3 x + 7\right) e^{- 3 x - 6}}{x^{2} + 4 x + 4}$$
-(7 + 3*x)*exp(-6 - 3*x)/(4 + x^2 + 4*x)
Combinatoria
[src]
-6 -3*x
-(7 + 3*x)*e *e
---------------------
2
(2 + x)
$$- \frac{\left(3 x + 7\right) e^{- 3 x}}{\left(x + 2\right)^{2} e^{6}}$$
-(7 + 3*x)*exp(-6)*exp(-3*x)/(2 + x)^2
Denominador racional
[src]
-6 - 3*x 2 -6 - 3*x
- (2 + x)*e - 3*(2 + x) *e
------------------------------------------
3
(2 + x)
$$\frac{- 3 \left(x + 2\right)^{2} e^{- 3 x - 6} - \left(x + 2\right) e^{- 3 x - 6}}{\left(x + 2\right)^{3}}$$
(-(2 + x)*exp(-6 - 3*x) - 3*(2 + x)^2*exp(-6 - 3*x))/(2 + x)^3
Unión de expresiones racionales
[src]
-6 - 3*x
(-7 - 3*x)*e
--------------------
2
(2 + x)
$$\frac{\left(- 3 x - 7\right) e^{- 3 x - 6}}{\left(x + 2\right)^{2}}$$
(-7 - 3*x)*exp(-6 - 3*x)/(2 + x)^2
Respuesta numérica
[src]
-0.25*exp(-6 - 3*x)/(1 + 0.5*x)^2 - 3.0*exp(-6 - 3*x)/(2.0 + x)
-0.25*exp(-6 - 3*x)/(1 + 0.5*x)^2 - 3.0*exp(-6 - 3*x)/(2.0 + x)
Compilar la expresión
[src]
-6 - 3*x -6 - 3*x
e 3*e
- --------- - -----------
2 2 + x
(2 + x)
$$- \frac{3 e^{- 3 x - 6}}{x + 2} - \frac{e^{- 3 x - 6}}{\left(x + 2\right)^{2}}$$
-exp(-6 - 3*x)/(2 + x)^2 - 3*exp(-6 - 3*x)/(2 + x)
Potencias
[src]
-6 - 3*x -6 - 3*x
e 3*e
- --------- - -----------
2 2 + x
(2 + x)
$$- \frac{3 e^{- 3 x - 6}}{x + 2} - \frac{e^{- 3 x - 6}}{\left(x + 2\right)^{2}}$$
-exp(-6 - 3*x)/(2 + x)^2 - 3*exp(-6 - 3*x)/(2 + x)
Denominador común
[src]
-(7 + 3*x) ------------------------------------ 6 3*x 2 6 3*x 6 3*x 4*e *e + x *e *e + 4*x*e *e
$$- \frac{3 x + 7}{x^{2} e^{6} e^{3 x} + 4 x e^{6} e^{3 x} + 4 e^{6} e^{3 x}}$$
-(7 + 3*x)/(4*exp(6)*exp(3*x) + x^2*exp(6)*exp(3*x) + 4*x*exp(6)*exp(3*x))
Parte trigonométrica
[src]
-6 - 3*x -6 - 3*x
e 3*e
- --------- - -----------
2 2 + x
(2 + x)
$$- \frac{3 e^{- 3 x - 6}}{x + 2} - \frac{e^{- 3 x - 6}}{\left(x + 2\right)^{2}}$$
-sinh(6 + 3*x) + cosh(6 + 3*x) 3*(-sinh(6 + 3*x) + cosh(6 + 3*x))
- ------------------------------ - ----------------------------------
2 2 + x
(2 + x)
$$- \frac{3 \left(- \sinh{\left(3 x + 6 \right)} + \cosh{\left(3 x + 6 \right)}\right)}{x + 2} - \frac{- \sinh{\left(3 x + 6 \right)} + \cosh{\left(3 x + 6 \right)}}{\left(x + 2\right)^{2}}$$
-cosh(6 + 3*x) + sinh(6 + 3*x) -3*sinh(6 + 3*x) + 3*cosh(6 + 3*x)
------------------------------ - ----------------------------------
2 2 + x
(2 + x)
$$- \frac{- 3 \sinh{\left(3 x + 6 \right)} + 3 \cosh{\left(3 x + 6 \right)}}{x + 2} + \frac{\sinh{\left(3 x + 6 \right)} - \cosh{\left(3 x + 6 \right)}}{\left(x + 2\right)^{2}}$$
-7*cosh(6 + 3*x) + 7*sinh(6 + 3*x) - 3*x*cosh(6 + 3*x) + 3*x*sinh(6 + 3*x)
--------------------------------------------------------------------------
2
(2 + x)
$$\frac{3 x \sinh{\left(3 x + 6 \right)} - 3 x \cosh{\left(3 x + 6 \right)} + 7 \sinh{\left(3 x + 6 \right)} - 7 \cosh{\left(3 x + 6 \right)}}{\left(x + 2\right)^{2}}$$
(-7*cosh(6 + 3*x) + 7*sinh(6 + 3*x) - 3*x*cosh(6 + 3*x) + 3*x*sinh(6 + 3*x))/(2 + x)^2