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VladaTkachuk
@VladaTkachuk
July 2022
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(2x^2- x-1)/(x^2-1)
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Dимасuk
Verified answer
Разложим сначала числитель. Для этого решим квадратное уравнение:
2x² - x - 1 = 0
D = 1 + 2•4 = 9 = 3²
x1 = (1 + 3)/4 = 1
x2 = (1 - 2)/4 = -1/2
Тогда 2x² - x - 1 = 2(x - 1)(x + 1/2) = (x - 1)(2x + 1).
Значит,
(2x² - x - 1)/(x² - 1) = (x - 1)(2x + 1)/(x - 1)(x + 1) = (2x + 1)/(x + 1).
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Answers & Comments
Verified answer
Разложим сначала числитель. Для этого решим квадратное уравнение:2x² - x - 1 = 0
D = 1 + 2•4 = 9 = 3²
x1 = (1 + 3)/4 = 1
x2 = (1 - 2)/4 = -1/2
Тогда 2x² - x - 1 = 2(x - 1)(x + 1/2) = (x - 1)(2x + 1).
Значит,
(2x² - x - 1)/(x² - 1) = (x - 1)(2x + 1)/(x - 1)(x + 1) = (2x + 1)/(x + 1).