Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(x^3/(x-6))*(x-6)*(-x^3/(2*(x-6)^2)+3*x^2/(2*(x-6)))/x^3
¿Cómo vas a descomponer esta sqrt(x^3/(x-6))*(x-6)*(-x^3/(2*(x-6)^2)+3*x^2/(2*(x-6)))/x^3 expresión en fracciones?
Solución
Ha introducido
[src]
_______
/ 3 / 3 2 \
/ x | -x 3*x |
/ ----- *(x - 6)*|---------- + ---------|
\/ x - 6 | 2 2*(x - 6)|
\2*(x - 6) /
---------------------------------------------
3
x
$$\frac{\sqrt{\frac{x^{3}}{x - 6}} \left(x - 6\right) \left(\frac{3 x^{2}}{2 \left(x - 6\right)} + \frac{\left(-1\right) x^{3}}{2 \left(x - 6\right)^{2}}\right)}{x^{3}}$$
((sqrt(x^3/(x - 6))*(x - 6))*((-x^3)/((2*(x - 6)^2)) + (3*x^2)/((2*(x - 6)))))/x^3
Simplificación general
[src]
________
/ 3
/ x
/ ------ *(-9 + x)
\/ -6 + x
----------------------
x*(-6 + x)
$$\frac{\sqrt{\frac{x^{3}}{x - 6}} \left(x - 9\right)}{x \left(x - 6\right)}$$
sqrt(x^3/(-6 + x))*(-9 + x)/(x*(-6 + x))
Respuesta numérica
[src]
(x^3/(-6.0 + x))^0.5*(-6.0 + x)*(3.0*x^2/(-12.0 + 2.0*x) - 0.0138888888888889*x^3/(-1 + 0.166666666666667*x)^2)/x^3
(x^3/(-6.0 + x))^0.5*(-6.0 + x)*(3.0*x^2/(-12.0 + 2.0*x) - 0.0138888888888889*x^3/(-1 + 0.166666666666667*x)^2)/x^3
Denominador racional
[src]
_______
/ 3
/ x / 3 2 2\
/ ----- *\- x *(-12 + 2*x) + 6*x *(-6 + x) /
\/ x - 6
------------------------------------------------
3
2*x *(-12 + 2*x)*(-6 + x)
$$\frac{\sqrt{\frac{x^{3}}{x - 6}} \left(- x^{3} \left(2 x - 12\right) + 6 x^{2} \left(x - 6\right)^{2}\right)}{2 x^{3} \left(x - 6\right) \left(2 x - 12\right)}$$
sqrt(x^3/(x - 6))*(-x^3*(-12 + 2*x) + 6*x^2*(-6 + x)^2)/(2*x^3*(-12 + 2*x)*(-6 + x))
Denominador común
[src]
________ ________
/ 3 / 3
/ x / x
- 9* / ------ + x* / ------
\/ -6 + x \/ -6 + x
-----------------------------------
2
x - 6*x
$$\frac{x \sqrt{\frac{x^{3}}{x - 6}} - 9 \sqrt{\frac{x^{3}}{x - 6}}}{x^{2} - 6 x}$$
(-9*sqrt(x^3/(-6 + x)) + x*sqrt(x^3/(-6 + x)))/(x^2 - 6*x)
Compilar la expresión
[src]
________
/ 3 / 2 3 \
/ x | 3*x x |
/ ------ *(-6 + x)*|--------- - -----------|
\/ -6 + x |-12 + 2*x 2|
\ 2*(-6 + x) /
------------------------------------------------
3
x
$$\frac{\sqrt{\frac{x^{3}}{x - 6}} \left(x - 6\right) \left(- \frac{x^{3}}{2 \left(x - 6\right)^{2}} + \frac{3 x^{2}}{2 x - 12}\right)}{x^{3}}$$
sqrt(x^3/(-6 + x))*(-6 + x)*(3*x^2/(-12 + 2*x) - x^3/(2*(-6 + x)^2))/x^3
Parte trigonométrica
[src]
________
/ 3 / 2 3 \
/ x | 3*x x |
/ ------ *(-6 + x)*|--------- - -----------|
\/ -6 + x |-12 + 2*x 2|
\ 2*(-6 + x) /
------------------------------------------------
3
x
$$\frac{\sqrt{\frac{x^{3}}{x - 6}} \left(x - 6\right) \left(- \frac{x^{3}}{2 \left(x - 6\right)^{2}} + \frac{3 x^{2}}{2 x - 12}\right)}{x^{3}}$$
sqrt(x^3/(-6 + x))*(-6 + x)*(3*x^2/(-12 + 2*x) - x^3/(2*(-6 + x)^2))/x^3
Combinatoria
[src]
________
/ 3
/ x
/ ------ *(-9 + x)
\/ -6 + x
----------------------
x*(-6 + x)
$$\frac{\sqrt{\frac{x^{3}}{x - 6}} \left(x - 9\right)}{x \left(x - 6\right)}$$
sqrt(x^3/(-6 + x))*(-9 + x)/(x*(-6 + x))
Potencias
[src]
________
/ 3 / 2 3 \
/ x | 3*x x |
/ ------ *(-6 + x)*|--------- - -----------|
\/ -6 + x |-12 + 2*x 2|
\ 2*(-6 + x) /
------------------------------------------------
3
x
$$\frac{\sqrt{\frac{x^{3}}{x - 6}} \left(x - 6\right) \left(- \frac{x^{3}}{2 \left(x - 6\right)^{2}} + \frac{3 x^{2}}{2 x - 12}\right)}{x^{3}}$$
sqrt(x^3/(-6 + x))*(-6 + x)*(3*x^2/(-12 + 2*x) - x^3/(2*(-6 + x)^2))/x^3
Unión de expresiones racionales
[src]
________
/ 3
/ x
/ ------ *(-9 + x)
\/ -6 + x
----------------------
x*(-6 + x)
$$\frac{\sqrt{\frac{x^{3}}{x - 6}} \left(x - 9\right)}{x \left(x - 6\right)}$$
sqrt(x^3/(-6 + x))*(-9 + x)/(x*(-6 + x))