175/MR00. zadatak / Matematika - Zbirka rešenih zadataka

MR-175. zadatak

Rešiti sledeću jednačinu:

$\frac{x}{x - 1} + \frac{x}{x + 1} = \frac{9}{4}$

$\frac{x}{x - 1} + \frac{x}{x + 1} = \frac{9}{4}$

\frac{x}{x - 1} + \frac{x}{x + 1} - \frac{9}{4} = 0

\frac{4 x (x + 1) + 4 x (x - 1) - 9 (x - 1) (x + 1)}{4 (x - 1) (x + 1)} = 0

$\frac{4 x^{2} + 4 x + 4 x^{2} - 4 x - 9 (x^{2} - 1^{2})}{4 (x - 1) (x + 1)} = 0$

\frac{8 x^{2} - 9 x^{2} + 9}{4 (x - 1) (x + 1)} = 0

\frac{- x^{2} + 9}{4 (x - 1) (x + 1)} = 0

- x^{2} + 9 = 0

$- x^{2} = - 9 | \cdot (- 1)$

x^{2} = 9

x = \pm \sqrt{9}

$x_{1} = 3; x_{2} = - 3$

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