Question

спростіть вираз (х+3/х2-1 - 1/х2+х)* х2-х/3х+3
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Answer 1

Ответ:

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