Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt((x^3-2*x^2)/(x-3))*(x-3)*((-4*x+3*x^2)/(2*(x-3))-(x^3-2*x^2)/(2*(x-3)^2))/(x^3-2*x^2)
¿Cómo vas a descomponer esta sqrt((x^3-2*x^2)/(x-3))*(x-3)*((-4*x+3*x^2)/(2*(x-3))-(x^3-2*x^2)/(2*(x-3)^2))/(x^3-2*x^2) expresión en fracciones?
Solución
Ha introducido
[src]
___________
/ 3 2 / 2 3 2 \
/ x - 2*x |-4*x + 3*x x - 2*x |
/ --------- *(x - 3)*|----------- - ----------|
\/ x - 3 | 2*(x - 3) 2|
\ 2*(x - 3) /
---------------------------------------------------
3 2
x - 2*x
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(- \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}} + \frac{3 x^{2} - 4 x}{2 \left(x - 3\right)}\right)}{x^{3} - 2 x^{2}}$$
((sqrt((x^3 - 2*x^2)/(x - 3))*(x - 3))*((-4*x + 3*x^2)/((2*(x - 3))) - (x^3 - 2*x^2)/(2*(x - 3)^2)))/(x^3 - 2*x^2)
Simplificación general
[src]
_____________
/ 2
/ x *(-2 + x) / 2 11*x\
/ ----------- *|6 + x - ----|
\/ -3 + x \ 2 /
----------------------------------
/ 2 \
x*\6 + x - 5*x/
$$\frac{\sqrt{\frac{x^{2} \left(x - 2\right)}{x - 3}} \left(x^{2} - \frac{11 x}{2} + 6\right)}{x \left(x^{2} - 5 x + 6\right)}$$
sqrt(x^2*(-2 + x)/(-3 + x))*(6 + x^2 - 11*x/2)/(x*(6 + x^2 - 5*x))
Respuesta numérica
[src]
((x^3 - 2.0*x^2)/(-3.0 + x))^0.5*(-3.0 + x)*((3.0*x^2 - 4.0*x)/(-6.0 + 2.0*x) - 0.0555555555555556*(x^3 - 2.0*x^2)/(-1 + 0.333333333333333*x)^2)/(x^3 - 2.0*x^2)
((x^3 - 2.0*x^2)/(-3.0 + x))^0.5*(-3.0 + x)*((3.0*x^2 - 4.0*x)/(-6.0 + 2.0*x) - 0.0555555555555556*(x^3 - 2.0*x^2)/(-1 + 0.333333333333333*x)^2)/(x^3 - 2.0*x^2)
Denominador racional
[src]
___________
/ 3 2
/ x - 2*x / / 3 2\ 2 / 2\\
/ --------- *\(-6 + 2*x)*\- x + 2*x / + 2*(-3 + x) *\-4*x + 3*x //
\/ x - 3
-----------------------------------------------------------------------
/ 3 2\
2*(-6 + 2*x)*(-3 + x)*\x - 2*x /
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(2 \left(x - 3\right)^{2} \left(3 x^{2} - 4 x\right) + \left(2 x - 6\right) \left(- x^{3} + 2 x^{2}\right)\right)}{2 \left(x - 3\right) \left(2 x - 6\right) \left(x^{3} - 2 x^{2}\right)}$$
sqrt((x^3 - 2*x^2)/(x - 3))*((-6 + 2*x)*(-x^3 + 2*x^2) + 2*(-3 + x)^2*(-4*x + 3*x^2))/(2*(-6 + 2*x)*(-3 + x)*(x^3 - 2*x^2))
Combinatoria
[src]
_____________
/ 2
/ x *(-2 + x)
/ ----------- *(-4 + x)*(-3 + 2*x)
\/ -3 + x
--------------------------------------
2*x*(-3 + x)*(-2 + x)
$$\frac{\sqrt{\frac{x^{2} \left(x - 2\right)}{x - 3}} \left(x - 4\right) \left(2 x - 3\right)}{2 x \left(x - 3\right) \left(x - 2\right)}$$
sqrt(x^2*(-2 + x)/(-3 + x))*(-4 + x)*(-3 + 2*x)/(2*x*(-3 + x)*(-2 + x))
Parte trigonométrica
[src]
___________
/ 3 2 / 2 3 2 \
/ x - 2*x |-4*x + 3*x x - 2*x |
/ --------- *(-3 + x)*|----------- - -----------|
\/ -3 + x | -6 + 2*x 2|
\ 2*(-3 + x) /
-----------------------------------------------------
3 2
x - 2*x
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 x - 6} - \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}}\right)}{x^{3} - 2 x^{2}}$$
sqrt((x^3 - 2*x^2)/(-3 + x))*(-3 + x)*((-4*x + 3*x^2)/(-6 + 2*x) - (x^3 - 2*x^2)/(2*(-3 + x)^2))/(x^3 - 2*x^2)
Compilar la expresión
[src]
___________
/ 3 2 / 2 3 2 \
/ x - 2*x |-4*x + 3*x x - 2*x |
/ --------- *(-3 + x)*|----------- - -----------|
\/ -3 + x | -6 + 2*x 2|
\ 2*(-3 + x) /
-----------------------------------------------------
3 2
x - 2*x
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 x - 6} - \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}}\right)}{x^{3} - 2 x^{2}}$$
sqrt((x^3 - 2*x^2)/(-3 + x))*(-3 + x)*((-4*x + 3*x^2)/(-6 + 2*x) - (x^3 - 2*x^2)/(2*(-3 + x)^2))/(x^3 - 2*x^2)
Unión de expresiones racionales
[src]
_____________
/ 2
/ x *(-2 + x)
/ ----------- *((-4 + 3*x)*(-3 + x) - x*(-2 + x))
\/ -3 + x
-----------------------------------------------------
2*x*(-3 + x)*(-2 + x)
$$\frac{\sqrt{\frac{x^{2} \left(x - 2\right)}{x - 3}} \left(- x \left(x - 2\right) + \left(x - 3\right) \left(3 x - 4\right)\right)}{2 x \left(x - 3\right) \left(x - 2\right)}$$
sqrt(x^2*(-2 + x)/(-3 + x))*((-4 + 3*x)*(-3 + x) - x*(-2 + x))/(2*x*(-3 + x)*(-2 + x))
Potencias
[src]
___________
/ 3 2 / 2 3 2 \
/ x - 2*x |-4*x + 3*x x - 2*x |
/ --------- *(-3 + x)*|----------- - -----------|
\/ -3 + x | -6 + 2*x 2|
\ 2*(-3 + x) /
-----------------------------------------------------
3 2
x - 2*x
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 x - 6} - \frac{x^{3} - 2 x^{2}}{2 \left(x - 3\right)^{2}}\right)}{x^{3} - 2 x^{2}}$$
/ 3 \
___________ | 2 x |
/ 3 2 | 2 x - -- |
/ x - 2*x |-4*x + 3*x 2 |
/ --------- *(-3 + x)*|----------- + ---------|
\/ -3 + x | -6 + 2*x 2|
\ (-3 + x) /
---------------------------------------------------
3 2
x - 2*x
$$\frac{\sqrt{\frac{x^{3} - 2 x^{2}}{x - 3}} \left(x - 3\right) \left(\frac{3 x^{2} - 4 x}{2 x - 6} + \frac{- \frac{x^{3}}{2} + x^{2}}{\left(x - 3\right)^{2}}\right)}{x^{3} - 2 x^{2}}$$
sqrt((x^3 - 2*x^2)/(-3 + x))*(-3 + x)*((-4*x + 3*x^2)/(-6 + 2*x) + (x^2 - x^3/2)/(-3 + x)^2)/(x^3 - 2*x^2)
Denominador común
[src]
_________________ _________________ _________________
/ 3 2 / 3 2 / 3 2
/ x 2*x / x 2*x 2 / x 2*x
12* / ------ - ------ - 11*x* / ------ - ------ + 2*x * / ------ - ------
\/ -3 + x -3 + x \/ -3 + x -3 + x \/ -3 + x -3 + x
-------------------------------------------------------------------------------------
2 3
- 10*x + 2*x + 12*x
$$\frac{2 x^{2} \sqrt{\frac{x^{3}}{x - 3} - \frac{2 x^{2}}{x - 3}} - 11 x \sqrt{\frac{x^{3}}{x - 3} - \frac{2 x^{2}}{x - 3}} + 12 \sqrt{\frac{x^{3}}{x - 3} - \frac{2 x^{2}}{x - 3}}}{2 x^{3} - 10 x^{2} + 12 x}$$
(12*sqrt(x^3/(-3 + x) - 2*x^2/(-3 + x)) - 11*x*sqrt(x^3/(-3 + x) - 2*x^2/(-3 + x)) + 2*x^2*sqrt(x^3/(-3 + x) - 2*x^2/(-3 + x)))/(-10*x^2 + 2*x^3 + 12*x)