Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x)/(x^2+5*x)+(-5-2*x)*exp(x)/(x^2+5*x)^2
¿Cómo vas a descomponer esta exp(x)/(x^2+5*x)+(-5-2*x)*exp(x)/(x^2+5*x)^2 expresión en fracciones?
Solución
Ha introducido
[src]
x x
e (-5 - 2*x)*e
-------- + -------------
2 2
x + 5*x / 2 \
\x + 5*x/
$$\frac{\left(- 2 x - 5\right) e^{x}}{\left(x^{2} + 5 x\right)^{2}} + \frac{e^{x}}{x^{2} + 5 x}$$
exp(x)/(x^2 + 5*x) + ((-5 - 2*x)*exp(x))/(x^2 + 5*x)^2
Simplificación general
[src]
x
(-5 - 2*x + x*(5 + x))*e
-------------------------
2 2
x *(5 + x)
$$\frac{\left(x \left(x + 5\right) - 2 x - 5\right) e^{x}}{x^{2} \left(x + 5\right)^{2}}$$
(-5 - 2*x + x*(5 + x))*exp(x)/(x^2*(5 + x)^2)
Combinatoria
[src]
/ 2 \ x
\-5 + x + 3*x/*e
------------------
2 2
x *(5 + x)
$$\frac{\left(x^{2} + 3 x - 5\right) e^{x}}{x^{2} \left(x + 5\right)^{2}}$$
(-5 + x^2 + 3*x)*exp(x)/(x^2*(5 + x)^2)
Denominador común
[src]
x 2 x x
- 5*e + x *e + 3*x*e
-----------------------
4 3 2
x + 10*x + 25*x
$$\frac{x^{2} e^{x} + 3 x e^{x} - 5 e^{x}}{x^{4} + 10 x^{3} + 25 x^{2}}$$
(-5*exp(x) + x^2*exp(x) + 3*x*exp(x))/(x^4 + 10*x^3 + 25*x^2)
Unión de expresiones racionales
[src]
x
(-5 - 2*x + x*(5 + x))*e
-------------------------
2 2
x *(5 + x)
$$\frac{\left(x \left(x + 5\right) - 2 x - 5\right) e^{x}}{x^{2} \left(x + 5\right)^{2}}$$
(-5 - 2*x + x*(5 + x))*exp(x)/(x^2*(5 + x)^2)
Respuesta numérica
[src]
exp(x)/(x^2 + 5.0*x) + 0.04*(-5.0 - 2.0*x)*exp(x)/(x + 0.2*x^2)^2
exp(x)/(x^2 + 5.0*x) + 0.04*(-5.0 - 2.0*x)*exp(x)/(x + 0.2*x^2)^2
Parte trigonométrica
[src]
cosh(x) + sinh(x) (5 + 2*x)*(cosh(x) + sinh(x))
----------------- - -----------------------------
2 2
x + 5*x / 2 \
\x + 5*x/
$$- \frac{\left(2 x + 5\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(x^{2} + 5 x\right)^{2}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{x^{2} + 5 x}$$
cosh(x) + sinh(x) (-5 - 2*x)*(cosh(x) + sinh(x))
----------------- + ------------------------------
2 2
x + 5*x / 2 \
\x + 5*x/
$$\frac{\left(- 2 x - 5\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(x^{2} + 5 x\right)^{2}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{x^{2} + 5 x}$$
(cosh(x) + sinh(x))/(x^2 + 5*x) + (-5 - 2*x)*(cosh(x) + sinh(x))/(x^2 + 5*x)^2
Denominador racional
[src]
2
/ 2 \ x / 2 \ x
\x + 5*x/ *e + (-5 - 2*x)*\x + 5*x/*e
-----------------------------------------
3
/ 2 \
\x + 5*x/
$$\frac{\left(- 2 x - 5\right) \left(x^{2} + 5 x\right) e^{x} + \left(x^{2} + 5 x\right)^{2} e^{x}}{\left(x^{2} + 5 x\right)^{3}}$$
((x^2 + 5*x)^2*exp(x) + (-5 - 2*x)*(x^2 + 5*x)*exp(x))/(x^2 + 5*x)^3