Решите пожалуйста уравнение 6/4x^2-9 - x-1/2x-3 = 3/2x+3. Created by Маргарита0505. algebra-ru

2x+3...

July 2022 1 20 Report

Решите пожалуйста уравнение
6/4x^2-9 - x-1/2x-3 = 3/2x+3

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obsessedcatlover $\frac{6}{4 x^{2} - 9} - \frac{x-1}{2x-3} = \frac{3}{2x+3}$
$\frac{6}{(2x+3)(2x-3)} - \frac{(x-1)(2x+3)}{(2x-3)(2x+3)} - \frac{3(2x-3)}{(2x+3)(2x-3)} = 0$
$\frac{6 - 2 x^{2} - x + 3 - 6x + 9}{(2x+3)(2x-3)} = 0$
$- \frac{2 x^{2} + 7x - 15}{(2x+3)(2x-3)} = 0$

Дробь равна нулю, когда числитель равен нулю ⇒
2x² + 7x - 15 = 0
D = 7² + 4*15*2 = 49 + 72 = 169 = 13²
x₁ = $\frac{-7 + 13}{4} = \frac{6}{4} = 1,5$
x₂ = $\frac{-7 - 13}{4} = -5$

Ответ: -5; 1,5

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