Sr Examen
¿Cómo vas a descomponer esta z/(x+y)+x/(z+y)+y/(z+x) expresión en fracciones?
Solución
Ha introducido
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z x y ----- + ----- + ----- x + y z + y z + x
$$\frac{y}{x + z} + \left(\frac{x}{y + z} + \frac{z}{x + y}\right)$$
z/(x + y) + x/(z + y) + y/(z + x)
Simplificación general
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x y z ----- + ----- + ----- y + z x + z x + y
$$\frac{x}{y + z} + \frac{y}{x + z} + \frac{z}{x + y}$$
x/(y + z) + y/(x + z) + z/(x + y)
Compilar la expresión
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x y z ----- + ----- + ----- y + z x + z x + y
$$\frac{x}{y + z} + \frac{y}{x + z} + \frac{z}{x + y}$$
x/(y + z) + y/(x + z) + z/(x + y)
Potencias
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x y z ----- + ----- + ----- y + z x + z x + y
$$\frac{x}{y + z} + \frac{y}{x + z} + \frac{z}{x + y}$$
x/(y + z) + y/(x + z) + z/(x + y)
Denominador racional
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(x + z)*(x*(x + y) + z*(y + z)) + y*(x + y)*(y + z)
---------------------------------------------------
(x + y)*(x + z)*(y + z)
$$\frac{y \left(x + y\right) \left(y + z\right) + \left(x + z\right) \left(x \left(x + y\right) + z \left(y + z\right)\right)}{\left(x + y\right) \left(x + z\right) \left(y + z\right)}$$
((x + z)*(x*(x + y) + z*(y + z)) + y*(x + y)*(y + z))/((x + y)*(x + z)*(y + z))
Unión de expresiones racionales
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(x + z)*(x*(x + y) + z*(y + z)) + y*(x + y)*(y + z)
---------------------------------------------------
(x + y)*(x + z)*(y + z)
$$\frac{y \left(x + y\right) \left(y + z\right) + \left(x + z\right) \left(x \left(x + y\right) + z \left(y + z\right)\right)}{\left(x + y\right) \left(x + z\right) \left(y + z\right)}$$
((x + z)*(x*(x + y) + z*(y + z)) + y*(x + y)*(y + z))/((x + y)*(x + z)*(y + z))
Denominador común
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3 3 3
x + y + z + x*y*z
1 + -------------------------------------------------
2 2 2 2 2 2
x*y + x*z + y*x + y*z + z*x + z*y + 2*x*y*z
$$\frac{x^{3} + x y z + y^{3} + z^{3}}{x^{2} y + x^{2} z + x y^{2} + 2 x y z + x z^{2} + y^{2} z + y z^{2}} + 1$$
1 + (x^3 + y^3 + z^3 + x*y*z)/(x*y^2 + x*z^2 + y*x^2 + y*z^2 + z*x^2 + z*y^2 + 2*x*y*z)
Parte trigonométrica
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x y z ----- + ----- + ----- y + z x + z x + y
$$\frac{x}{y + z} + \frac{y}{x + z} + \frac{z}{x + y}$$
x/(y + z) + y/(x + z) + z/(x + y)
Combinatoria
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3 3 3 2 2 2 2 2 2
x + y + z + x*y + x*z + y*x + y*z + z*x + z*y + 3*x*y*z
----------------------------------------------------------------
(x + y)*(x + z)*(y + z)
$$\frac{x^{3} + x^{2} y + x^{2} z + x y^{2} + 3 x y z + x z^{2} + y^{3} + y^{2} z + y z^{2} + z^{3}}{\left(x + y\right) \left(x + z\right) \left(y + z\right)}$$
(x^3 + y^3 + z^3 + x*y^2 + x*z^2 + y*x^2 + y*z^2 + z*x^2 + z*y^2 + 3*x*y*z)/((x + y)*(x + z)*(y + z))