Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
(y-x/(y+x))*((x+3*y/(x-y))-y/x)
¿Cómo vas a descomponer esta (y-x/(y+x))*((x+3*y/(x-y))-y/x) expresión en fracciones?
Solución
Ha introducido
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/ x \ / 3*y y\ |y - -----|*|x + ----- - -| \ y + x/ \ x - y x/
$$\left(- \frac{x}{x + y} + y\right) \left(\left(x + \frac{3 y}{x - y}\right) - \frac{y}{x}\right)$$
(y - x/(y + x))*(x + (3*y)/(x - y) - y/x)
Simplificación general
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/ x \ / y 3*y \ -|-y + -----|*|x - - + -----| \ x + y/ \ x x - y/
$$- \left(\frac{x}{x + y} - y\right) \left(x + \frac{3 y}{x - y} - \frac{y}{x}\right)$$
-(-y + x/(x + y))*(x - y/x + 3*y/(x - y))
Respuesta numérica
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(y - x/(x + y))*(x - y/x + 3.0*y/(x - y))
(y - x/(x + y))*(x - y/x + 3.0*y/(x - y))
Denominador común
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4 2 2 2 2 3
y + x *y - x*y - 2*y*x + 4*x*y
y - x + x*y + -----------------------------------
3 2
x - x*y
$$x y - x + y + \frac{x^{2} y^{2} - 2 x^{2} y + 4 x y^{3} - x y^{2} + y^{4}}{x^{3} - x y^{2}}$$
y - x + x*y + (y^4 + x^2*y^2 - x*y^2 - 2*y*x^2 + 4*x*y^3)/(x^3 - x*y^2)
Parte trigonométrica
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/ x \ / y 3*y \ |y - -----|*|x - - + -----| \ x + y/ \ x x - y/
$$\left(- \frac{x}{x + y} + y\right) \left(x + \frac{3 y}{x - y} - \frac{y}{x}\right)$$
(y - x/(x + y))*(x - y/x + 3*y/(x - y))
Denominador racional
[src]
(-x + y*(x + y))*(x*(3*y + x*(x - y)) - y*(x - y))
--------------------------------------------------
x*(x + y)*(x - y)
$$\frac{\left(- x + y \left(x + y\right)\right) \left(x \left(x \left(x - y\right) + 3 y\right) - y \left(x - y\right)\right)}{x \left(x - y\right) \left(x + y\right)}$$
(-x + y*(x + y))*(x*(3*y + x*(x - y)) - y*(x - y))/(x*(x + y)*(x - y))
Compilar la expresión
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/ x \ / y 3*y \ |y - -----|*|x - - + -----| \ x + y/ \ x x - y/
$$\left(- \frac{x}{x + y} + y\right) \left(x + \frac{3 y}{x - y} - \frac{y}{x}\right)$$
/ / 1 3 \\ / x \ |x + y*|- - + -----||*|y - -----| \ \ x x - y// \ x + y/
$$\left(x + y \left(\frac{3}{x - y} - \frac{1}{x}\right)\right) \left(- \frac{x}{x + y} + y\right)$$
(x + y*(-1/x + 3/(x - y)))*(y - x/(x + y))
Unión de expresiones racionales
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(-x + y*(x + y))*(x*(3*y + x*(x - y)) - y*(x - y))
--------------------------------------------------
x*(x + y)*(x - y)
$$\frac{\left(- x + y \left(x + y\right)\right) \left(x \left(x \left(x - y\right) + 3 y\right) - y \left(x - y\right)\right)}{x \left(x - y\right) \left(x + y\right)}$$
(-x + y*(x + y))*(x*(3*y + x*(x - y)) - y*(x - y))/(x*(x + y)*(x - y))
Combinatoria
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/ 2 \ / 3 2 2 \
\y - x + x*y/*\x + y - y*x + 2*x*y/
---------------------------------------
x*(x + y)*(x - y)
$$\frac{\left(x y - x + y^{2}\right) \left(x^{3} - x^{2} y + 2 x y + y^{2}\right)}{x \left(x - y\right) \left(x + y\right)}$$
(y^2 - x + x*y)*(x^3 + y^2 - y*x^2 + 2*x*y)/(x*(x + y)*(x - y))
Potencias
[src]
/ x \ / y 3*y \ |y - -----|*|x - - + -----| \ x + y/ \ x x - y/
$$\left(- \frac{x}{x + y} + y\right) \left(x + \frac{3 y}{x - y} - \frac{y}{x}\right)$$
(y - x/(x + y))*(x - y/x + 3*y/(x - y))