Question

Сократите дробь 7х2+11х-6/9-49х2

Answer 1

Разложим дробь из числителя:
7х² + 11х - 6 = 0
D = 11² - 4 * 7 * (-6) = 289
х₁ = $frac{-11+ sqrt {289}}{2*7}$ = 3/7
х₂ = $frac{-11- sqrt {289}}{2*7}$ = - 2
7х² + 11х - 6 = 7 (x - 3/7)(x - 2) = (7x - 3)(x - 2) = - (3 - 7x)(x - 2)

$frac{- (3-7x)(x-2)}{9-49x^{2}} = frac{-(3-7x)(x-2)}{(3-7x)(3+7x)} = frac{-(x-2)}{3+7x} = frac{2-x}{3+7x}$

Ответ: $frac{2-x}{3+7x}$