Question

упростите
$( \frac{x + 2}{x - 2} - \frac{x}{x + 2}) \times \frac{ x - 2}{3x + 2}$
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Answer 1

$( \frac{x + 2}{x - 2} - \frac{x}{x + 2} ) \times \frac{x - 2}{3x + 2} = \frac{2}{x + 2} \\ \\ 1) \ \frac{x + 2}{x - 2} - \frac{x}{x + 2} = \frac{(x + 2)(x + 2) - x(x - 2)}{(x - 2)(x + 2)} = \frac{x {}^{2} + 4x + 4 - x {}^{2} + 2x}{(x - 2)(x + 2)} = \frac{6x + 4}{(x - 2)(x + 2)} = \frac{2(3x + 2)}{(x + 2)(x - 2)}\\\\ 2) \: \frac{2(3x + 2) \times (x - 2)}{(x + 2)(x - 2) \times (3x + 2)} = \frac{2}{x + 2}$