Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
-z^3-(-1)*z^(2*y)*(-x)*z/(z^2+x*y)-y^(2*x)*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
¿Cómo vas a descomponer esta -z^3-(-1)*z^(2*y)*(-x)*z/(z^2+x*y)-y^(2*x)*(-x)*z/((z^2+x*y)*((z^2+x*y)^2)) expresión en fracciones?
Solución
Ha introducido
[src]
2*y 2*x
3 -z *(-x)*z y *(-x)*z
- z - ------------ - ----------------------
2 2
z + x*y / 2 \ / 2 \
\z + x*y/*\z + x*y/
$$\left(- z^{3} - \frac{z - x \left(- z^{2 y}\right)}{x y + z^{2}}\right) - \frac{z - x y^{2 x}}{\left(x y + z^{2}\right) \left(x y + z^{2}\right)^{2}}$$
-z^3 - ((-z^(2*y))*(-x))*z/(z^2 + x*y) - (y^(2*x)*(-x))*z/((z^2 + x*y)*(z^2 + x*y)^2)
Simplificación general
[src]
2*x 2*y
3 x*z*y x*z*z
- z + ----------- - --------
3 2
/ 2 \ z + x*y
\z + x*y/
$$\frac{x y^{2 x} z}{\left(x y + z^{2}\right)^{3}} - \frac{x z z^{2 y}}{x y + z^{2}} - z^{3}$$
-z^3 + x*z*y^(2*x)/(z^2 + x*y)^3 - x*z*z^(2*y)/(z^2 + x*y)
Respuesta numérica
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-z^3 + x*z*y^(2.0*x)/(z^2 + x*y)^3 - x*z*z^(2.0*y)/(z^2 + x*y)
-z^3 + x*z*y^(2.0*x)/(z^2 + x*y)^3 - x*z*z^(2.0*y)/(z^2 + x*y)
Compilar la expresión
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/ 2*x 2*y \
3 | x*y x*z |
- z + z*|----------- - --------|
| 3 2 |
|/ 2 \ z + x*y|
\\z + x*y/ /
$$- z^{3} + z \left(\frac{x y^{2 x}}{\left(x y + z^{2}\right)^{3}} - \frac{x z^{2 y}}{x y + z^{2}}\right)$$
2*x 2*y
3 x*z*y x*z*z
- z + ----------- - --------
3 2
/ 2 \ z + x*y
\z + x*y/
$$\frac{x y^{2 x} z}{\left(x y + z^{2}\right)^{3}} - \frac{x z z^{2 y}}{x y + z^{2}} - z^{3}$$
/ 2*x 2*y \
3 | z*y z*z |
- z + x*|----------- - --------|
| 3 2 |
|/ 2 \ z + x*y|
\\z + x*y/ /
$$x \left(\frac{y^{2 x} z}{\left(x y + z^{2}\right)^{3}} - \frac{z z^{2 y}}{x y + z^{2}}\right) - z^{3}$$
-z^3 + x*(z*y^(2*x)/(z^2 + x*y)^3 - z*z^(2*y)/(z^2 + x*y))
Denominador racional
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3
/ 2 \ / 3 / 2 \ 2*y\ 2*x / 2 \
\z + x*y/ *\- z *\z + x*y/ - x*z*z / + x*z*y *\z + x*y/
--------------------------------------------------------------
4
/ 2 \
\z + x*y/
$$\frac{x y^{2 x} z \left(x y + z^{2}\right) + \left(x y + z^{2}\right)^{3} \left(- x z z^{2 y} - z^{3} \left(x y + z^{2}\right)\right)}{\left(x y + z^{2}\right)^{4}}$$
((z^2 + x*y)^3*(-z^3*(z^2 + x*y) - x*z*z^(2*y)) + x*z*y^(2*x)*(z^2 + x*y))/(z^2 + x*y)^4
Denominador común
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5 2*y 2*x 3 2 2*y 2 3 2*y
3 x*z *z - x*z*y + z*x *y *z + 2*y*x *z *z
- z - ----------------------------------------------------
6 3 3 4 2 2 2
z + x *y + 3*x*y*z + 3*x *y *z
$$- z^{3} - \frac{x^{3} y^{2} z z^{2 y} + 2 x^{2} y z^{3} z^{2 y} - x y^{2 x} z + x z^{5} z^{2 y}}{x^{3} y^{3} + 3 x^{2} y^{2} z^{2} + 3 x y z^{4} + z^{6}}$$
-z^3 - (x*z^5*z^(2*y) - x*z*y^(2*x) + z*x^3*y^2*z^(2*y) + 2*y*x^2*z^3*z^(2*y))/(z^6 + x^3*y^3 + 3*x*y*z^4 + 3*x^2*y^2*z^2)
Unión de expresiones racionales
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/ 2 \
| 2*x / 2 \ / 2*y 2 / 2 \\|
z*\x*y + \z + x*y/ *\- x*z - z *\z + x*y///
---------------------------------------------------
3
/ 2 \
\z + x*y/
$$\frac{z \left(x y^{2 x} + \left(x y + z^{2}\right)^{2} \left(- x z^{2 y} - z^{2} \left(x y + z^{2}\right)\right)\right)}{\left(x y + z^{2}\right)^{3}}$$
z*(x*y^(2*x) + (z^2 + x*y)^2*(-x*z^(2*y) - z^2*(z^2 + x*y)))/(z^2 + x*y)^3
Potencias
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2*x 2*y
3 x*z*y x*z*z
- z + ----------- - --------
3 2
/ 2 \ z + x*y
\z + x*y/
$$\frac{x y^{2 x} z}{\left(x y + z^{2}\right)^{3}} - \frac{x z z^{2 y}}{x y + z^{2}} - z^{3}$$
1 + 2*y 2*x
3 x*z x*z*y
- z - ---------- + -----------
2 3
z + x*y / 2 \
\z + x*y/
$$\frac{x y^{2 x} z}{\left(x y + z^{2}\right)^{3}} - \frac{x z^{2 y + 1}}{x y + z^{2}} - z^{3}$$
x y
/ 2\ / 2\
3 x*z*\y / x*z*\z /
- z + ----------- - ---------
3 2
/ 2 \ z + x*y
\z + x*y/
$$- \frac{x z \left(z^{2}\right)^{y}}{x y + z^{2}} + \frac{x z \left(y^{2}\right)^{x}}{\left(x y + z^{2}\right)^{3}} - z^{3}$$
-z^3 + x*z*(y^2)^x/(z^2 + x*y)^3 - x*z*(z^2)^y/(z^2 + x*y)
Parte trigonométrica
[src]
2*x 2*y
3 x*z*y x*z*z
- z + ----------- - --------
3 2
/ 2 \ z + x*y
\z + x*y/
$$\frac{x y^{2 x} z}{\left(x y + z^{2}\right)^{3}} - \frac{x z z^{2 y}}{x y + z^{2}} - z^{3}$$
-z^3 + x*z*y^(2*x)/(z^2 + x*y)^3 - x*z*z^(2*y)/(z^2 + x*y)
Combinatoria
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/ 8 2*x 4 2*y 3 2 2*y 3 3 2 6 2 2 4 2 2 2*y\
-z*\z - x*y + x*z *z + x *y *z + x *y *z + 3*x*y*z + 3*x *y *z + 2*y*x *z *z /
----------------------------------------------------------------------------------------------
3
/ 2 \
\z + x*y/
$$- \frac{z \left(x^{3} y^{3} z^{2} + x^{3} y^{2} z^{2 y} + 3 x^{2} y^{2} z^{4} + 2 x^{2} y z^{2} z^{2 y} + 3 x y z^{6} - x y^{2 x} + x z^{4} z^{2 y} + z^{8}\right)}{\left(x y + z^{2}\right)^{3}}$$
-z*(z^8 - x*y^(2*x) + x*z^4*z^(2*y) + x^3*y^2*z^(2*y) + x^3*y^3*z^2 + 3*x*y*z^6 + 3*x^2*y^2*z^4 + 2*y*x^2*z^2*z^(2*y))/(z^2 + x*y)^3