Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x*t)*(-2)/(x/5+1)^2+10*t*exp(x*t)/(x/5+1)
¿Cómo vas a descomponer esta exp(x*t)*(-2)/(x/5+1)^2+10*t*exp(x*t)/(x/5+1) expresión en fracciones?
Solución
Ha introducido
[src]
x*t x*t
e *(-2) 10*t*e
--------- + ---------
2 x
/x \ - + 1
|- + 1| 5
\5 /
$$\frac{\left(-2\right) e^{t x}}{\left(\frac{x}{5} + 1\right)^{2}} + \frac{10 t e^{t x}}{\frac{x}{5} + 1}$$
(exp(x*t)*(-2))/(x/5 + 1)^2 + ((10*t)*exp(x*t))/(x/5 + 1)
Simplificación general
[src]
/ 2\ t*x
50*\-5 - x + t*(5 + x) /*e
-----------------------------
3
(5 + x)
$$\frac{50 \left(t \left(x + 5\right)^{2} - x - 5\right) e^{t x}}{\left(x + 5\right)^{3}}$$
50*(-5 - x + t*(5 + x)^2)*exp(t*x)/(5 + x)^3
Respuesta numérica
[src]
-2.0*exp(x*t)/(1.0 + 0.2*x)^2 + 10.0*t*exp(x*t)/(1.0 + 0.2*x)
-2.0*exp(x*t)/(1.0 + 0.2*x)^2 + 10.0*t*exp(x*t)/(1.0 + 0.2*x)
Compilar la expresión
[src]
x*t x*t
2*e 10*t*e
- -------- + ---------
2 x
/ x\ 1 + -
|1 + -| 5
\ 5/
$$\frac{10 t e^{t x}}{\frac{x}{5} + 1} - \frac{2 e^{t x}}{\left(\frac{x}{5} + 1\right)^{2}}$$
-2*exp(x*t)/(1 + x/5)^2 + 10*t*exp(x*t)/(1 + x/5)
Unión de expresiones racionales
[src]
t*x
50*(-1 + t*(5 + x))*e
------------------------
2
(5 + x)
$$\frac{50 \left(t \left(x + 5\right) - 1\right) e^{t x}}{\left(x + 5\right)^{2}}$$
50*(-1 + t*(5 + x))*exp(t*x)/(5 + x)^2
Potencias
[src]
t*x t*x
2*e 10*t*e
- -------- + ---------
2 x
/ x\ 1 + -
|1 + -| 5
\ 5/
$$\frac{10 t e^{t x}}{\frac{x}{5} + 1} - \frac{2 e^{t x}}{\left(\frac{x}{5} + 1\right)^{2}}$$
-2*exp(t*x)/(1 + x/5)^2 + 10*t*exp(t*x)/(1 + x/5)
Denominador racional
[src]
t*x t*x 2 t*x
- 250*e - 50*x*e + 50*t*(5 + x) *e
-------------------------------------------
3
(5 + x)
$$\frac{50 t \left(x + 5\right)^{2} e^{t x} - 50 x e^{t x} - 250 e^{t x}}{\left(x + 5\right)^{3}}$$
(-250*exp(t*x) - 50*x*exp(t*x) + 50*t*(5 + x)^2*exp(t*x))/(5 + x)^3
Combinatoria
[src]
t*x
50*(-1 + 5*t + t*x)*e
------------------------
2
(5 + x)
$$\frac{50 \left(t x + 5 t - 1\right) e^{t x}}{\left(x + 5\right)^{2}}$$
50*(-1 + 5*t + t*x)*exp(t*x)/(5 + x)^2
Denominador común
[src]
t*x t*x t*x
- 50*e + 250*t*e + 50*t*x*e
------------------------------------
2
25 + x + 10*x
$$\frac{50 t x e^{t x} + 250 t e^{t x} - 50 e^{t x}}{x^{2} + 10 x + 25}$$
(-50*exp(t*x) + 250*t*exp(t*x) + 50*t*x*exp(t*x))/(25 + x^2 + 10*x)
Parte trigonométrica
[src]
2*(cosh(t*x) + sinh(t*x)) 10*t*(cosh(t*x) + sinh(t*x))
- ------------------------- + ----------------------------
2 x
/ x\ 1 + -
|1 + -| 5
\ 5/
$$\frac{10 t \left(\sinh{\left(t x \right)} + \cosh{\left(t x \right)}\right)}{\frac{x}{5} + 1} - \frac{2 \left(\sinh{\left(t x \right)} + \cosh{\left(t x \right)}\right)}{\left(\frac{x}{5} + 1\right)^{2}}$$
t*x t*x
2*e 10*t*e
- -------- + ---------
2 x
/ x\ 1 + -
|1 + -| 5
\ 5/
$$\frac{10 t e^{t x}}{\frac{x}{5} + 1} - \frac{2 e^{t x}}{\left(\frac{x}{5} + 1\right)^{2}}$$
-2*cosh(t*x) - 2*sinh(t*x) 10*t*(cosh(t*x) + sinh(t*x))
-------------------------- + ----------------------------
2 x
/ x\ 1 + -
|1 + -| 5
\ 5/
$$\frac{10 t \left(\sinh{\left(t x \right)} + \cosh{\left(t x \right)}\right)}{\frac{x}{5} + 1} + \frac{- 2 \sinh{\left(t x \right)} - 2 \cosh{\left(t x \right)}}{\left(\frac{x}{5} + 1\right)^{2}}$$
2*cosh(t*x) + 2*sinh(t*x) 10*t*(cosh(t*x) + sinh(t*x))
- ------------------------- + ----------------------------
2 x
/ x\ 1 + -
|1 + -| 5
\ 5/
$$\frac{10 t \left(\sinh{\left(t x \right)} + \cosh{\left(t x \right)}\right)}{\frac{x}{5} + 1} - \frac{2 \sinh{\left(t x \right)} + 2 \cosh{\left(t x \right)}}{\left(\frac{x}{5} + 1\right)^{2}}$$
-(2*cosh(t*x) + 2*sinh(t*x))/(1 + x/5)^2 + 10*t*(cosh(t*x) + sinh(t*x))/(1 + x/5)