Ecuaciones Racionales

ecuaciones
ecuaciones_racionales

Resuelve la ecuación:
$\frac{2(x+1)}{3(x-2)} + \frac{4}{x} = 4$

SOLUCIÓN

$\frac{2(x+1)}{3(x-2)} + \frac{4}{x} = \frac{4}{1}$

$m.c.m. \longrightarrow 3\cdot (x-2) \cdot x$

$\frac{x \cdot 2(x+1)}{3(x-2)x} + \frac{3(x-2) \cdot 4}{3(x-2)x} = \frac{3(x-2)x \cdot 4}{3(x-2)x}$

$x \cdot 2(x+1) + 3(x-2) \cdot 4 = 3(x-2)x \cdot 4$

$\begin{array}{ccc} & & x_1 = \frac{-38+22}{-20}=\frac{-4}{-5}\\ & \nearrow &\\ x=\frac{-38\pm \sqrt{38^2-4 \cdot(-10)\cdot(-24)}}{2 \cdot(-10)}= \frac{-38\pm \sqrt{484}}{-20}& &\\ & \searrow &\\& &x_2 = \frac{-38-22}{-20}=3\end{array}$

$\fbox{x=3}$ y $\fbox{x=4/5}$

SOLUCIÓN

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