Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(x^3/(x-3))*(x-3)*(-x^3/(2*(x-3)^2)+3*x^2/(2*(x-3)))/x^3
¿Cómo vas a descomponer esta sqrt(x^3/(x-3))*(x-3)*(-x^3/(2*(x-3)^2)+3*x^2/(2*(x-3)))/x^3 expresión en fracciones?
Solución
Ha introducido
[src]
_______
/ 3 / 3 2 \
/ x | -x 3*x |
/ ----- *(x - 3)*|---------- + ---------|
\/ x - 3 | 2 2*(x - 3)|
\2*(x - 3) /
---------------------------------------------
3
x
$$\frac{\sqrt{\frac{x^{3}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2}}{2 \left(x - 3\right)} + \frac{\left(-1\right) x^{3}}{2 \left(x - 3\right)^{2}}\right)}{x^{3}}$$
((sqrt(x^3/(x - 3))*(x - 3))*((-x^3)/((2*(x - 3)^2)) + (3*x^2)/((2*(x - 3)))))/x^3
Simplificación general
[src]
________
/ 3
/ x
/ ------ *(-9/2 + x)
\/ -3 + x
------------------------
x*(-3 + x)
$$\frac{\sqrt{\frac{x^{3}}{x - 3}} \left(x - \frac{9}{2}\right)}{x \left(x - 3\right)}$$
sqrt(x^3/(-3 + x))*(-9/2 + x)/(x*(-3 + x))
Unión de expresiones racionales
[src]
________
/ 3
/ x
/ ------ *(-9 + 2*x)
\/ -3 + x
------------------------
2*x*(-3 + x)
$$\frac{\sqrt{\frac{x^{3}}{x - 3}} \left(2 x - 9\right)}{2 x \left(x - 3\right)}$$
sqrt(x^3/(-3 + x))*(-9 + 2*x)/(2*x*(-3 + x))
Parte trigonométrica
[src]
________
/ 3 / 2 3 \
/ x | 3*x x |
/ ------ *(-3 + x)*|-------- - -----------|
\/ -3 + x |-6 + 2*x 2|
\ 2*(-3 + x) /
-----------------------------------------------
3
x
$$\frac{\sqrt{\frac{x^{3}}{x - 3}} \left(x - 3\right) \left(- \frac{x^{3}}{2 \left(x - 3\right)^{2}} + \frac{3 x^{2}}{2 x - 6}\right)}{x^{3}}$$
sqrt(x^3/(-3 + x))*(-3 + x)*(3*x^2/(-6 + 2*x) - x^3/(2*(-3 + x)^2))/x^3
Respuesta numérica
[src]
(x^3/(-3.0 + x))^0.5*(-3.0 + x)*(3.0*x^2/(-6.0 + 2.0*x) - 0.0555555555555556*x^3/(-1 + 0.333333333333333*x)^2)/x^3
(x^3/(-3.0 + x))^0.5*(-3.0 + x)*(3.0*x^2/(-6.0 + 2.0*x) - 0.0555555555555556*x^3/(-1 + 0.333333333333333*x)^2)/x^3
Denominador común
[src]
________ ________
/ 3 / 3
/ x / x
- 9* / ------ + 2*x* / ------
\/ -3 + x \/ -3 + x
-------------------------------------
2
-6*x + 2*x
$$\frac{2 x \sqrt{\frac{x^{3}}{x - 3}} - 9 \sqrt{\frac{x^{3}}{x - 3}}}{2 x^{2} - 6 x}$$
(-9*sqrt(x^3/(-3 + x)) + 2*x*sqrt(x^3/(-3 + x)))/(-6*x + 2*x^2)
Denominador racional
[src]
_______
/ 3
/ x / 3 2 2\
/ ----- *\- x *(-6 + 2*x) + 6*x *(-3 + x) /
\/ x - 3
-----------------------------------------------
3
2*x *(-6 + 2*x)*(-3 + x)
$$\frac{\sqrt{\frac{x^{3}}{x - 3}} \left(- x^{3} \left(2 x - 6\right) + 6 x^{2} \left(x - 3\right)^{2}\right)}{2 x^{3} \left(x - 3\right) \left(2 x - 6\right)}$$
sqrt(x^3/(x - 3))*(-x^3*(-6 + 2*x) + 6*x^2*(-3 + x)^2)/(2*x^3*(-6 + 2*x)*(-3 + x))
Compilar la expresión
[src]
________
/ 3 / 2 3 \
/ x | 3*x x |
/ ------ *(-3 + x)*|-------- - -----------|
\/ -3 + x |-6 + 2*x 2|
\ 2*(-3 + x) /
-----------------------------------------------
3
x
$$\frac{\sqrt{\frac{x^{3}}{x - 3}} \left(x - 3\right) \left(- \frac{x^{3}}{2 \left(x - 3\right)^{2}} + \frac{3 x^{2}}{2 x - 6}\right)}{x^{3}}$$
sqrt(x^3/(-3 + x))*(-3 + x)*(3*x^2/(-6 + 2*x) - x^3/(2*(-3 + x)^2))/x^3
Potencias
[src]
________
/ 3 / 2 3 \
/ x | 3*x x |
/ ------ *(-3 + x)*|-------- - -----------|
\/ -3 + x |-6 + 2*x 2|
\ 2*(-3 + x) /
-----------------------------------------------
3
x
$$\frac{\sqrt{\frac{x^{3}}{x - 3}} \left(x - 3\right) \left(- \frac{x^{3}}{2 \left(x - 3\right)^{2}} + \frac{3 x^{2}}{2 x - 6}\right)}{x^{3}}$$
sqrt(x^3/(-3 + x))*(-3 + x)*(3*x^2/(-6 + 2*x) - x^3/(2*(-3 + x)^2))/x^3
Combinatoria
[src]
________
/ 3
/ x
/ ------ *(-9 + 2*x)
\/ -3 + x
------------------------
2*x*(-3 + x)
$$\frac{\sqrt{\frac{x^{3}}{x - 3}} \left(2 x - 9\right)}{2 x \left(x - 3\right)}$$
sqrt(x^3/(-3 + x))*(-9 + 2*x)/(2*x*(-3 + x))