Question

спростіть вираз (1/x^2-4x+4 - 1/4-x^2) ÷ 2x/x^2-4​

Answer 1

Ответ:

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