Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x)/(x^3+5)-3*x^2*exp(x)/(x^3+5)^2
¿Cómo vas a descomponer esta exp(x)/(x^3+5)-3*x^2*exp(x)/(x^3+5)^2 expresión en fracciones?
Solución
Ha introducido
[src]
x 2 x
e 3*x *e
------ - ---------
3 2
x + 5 / 3 \
\x + 5/
$$- \frac{3 x^{2} e^{x}}{\left(x^{3} + 5\right)^{2}} + \frac{e^{x}}{x^{3} + 5}$$
exp(x)/(x^3 + 5) - (3*x^2)*exp(x)/(x^3 + 5)^2
Simplificación general
[src]
/ 3 2\ x
\5 + x - 3*x /*e
------------------
6 3
25 + x + 10*x
$$\frac{\left(x^{3} - 3 x^{2} + 5\right) e^{x}}{x^{6} + 10 x^{3} + 25}$$
(5 + x^3 - 3*x^2)*exp(x)/(25 + x^6 + 10*x^3)
Respuesta numérica
[src]
exp(x)/(5.0 + x^3) - 0.12*x^2*exp(x)/(1 + 0.2*x^3)^2
exp(x)/(5.0 + x^3) - 0.12*x^2*exp(x)/(1 + 0.2*x^3)^2
Unión de expresiones racionales
[src]
/ 3 2\ x
\5 + x - 3*x /*e
------------------
2
/ 3\
\5 + x /
$$\frac{\left(x^{3} - 3 x^{2} + 5\right) e^{x}}{\left(x^{3} + 5\right)^{2}}$$
(5 + x^3 - 3*x^2)*exp(x)/(5 + x^3)^2
Denominador racional
[src]
2
/ 3\ x 2 / 3\ x
\5 + x / *e - 3*x *\5 + x /*e
-------------------------------
3
/ 3\
\5 + x /
$$\frac{- 3 x^{2} \left(x^{3} + 5\right) e^{x} + \left(x^{3} + 5\right)^{2} e^{x}}{\left(x^{3} + 5\right)^{3}}$$
((5 + x^3)^2*exp(x) - 3*x^2*(5 + x^3)*exp(x))/(5 + x^3)^3
Combinatoria
[src]
/ 3 2\ x
\5 + x - 3*x /*e
------------------
2
/ 3\
\5 + x /
$$\frac{\left(x^{3} - 3 x^{2} + 5\right) e^{x}}{\left(x^{3} + 5\right)^{2}}$$
(5 + x^3 - 3*x^2)*exp(x)/(5 + x^3)^2
Denominador común
[src]
x 3 x 2 x
5*e + x *e - 3*x *e
----------------------
6 3
25 + x + 10*x
$$\frac{x^{3} e^{x} - 3 x^{2} e^{x} + 5 e^{x}}{x^{6} + 10 x^{3} + 25}$$
(5*exp(x) + x^3*exp(x) - 3*x^2*exp(x))/(25 + x^6 + 10*x^3)
Parte trigonométrica
[src]
2
cosh(x) + sinh(x) 3*x *(cosh(x) + sinh(x))
----------------- - ------------------------
3 2
5 + x / 3\
\5 + x /
$$- \frac{3 x^{2} \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(x^{3} + 5\right)^{2}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{x^{3} + 5}$$
(cosh(x) + sinh(x))/(5 + x^3) - 3*x^2*(cosh(x) + sinh(x))/(5 + x^3)^2