Найдите корни уравнения ((5x+4)/(3x^2+9x))-((6-7x)/(x^2-3x))=((3x+1)/(9-x^2)). Created by andreevvv641. algebra-ru

(9-x^2))...

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August 2022 1 17 Report

Найдите корни уравнения ((5x+4)/(3x^2+9x))-((6-7x)/(x^2-3x))=((3x+1)/(9-x^2))

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Dимасuk

Verified answer

(5x + 4)/(3x(x + 3) - (6 - 7x)/(x(x - 3) = (3x + 1)/(3 - x)(3 + x)
(5x + 4)/3x(x + 3) + (6 - 7x)/x(3 - x) = (3x + 1)/(3 - x)(3 + x)
ОДЗ:
x ≠ 0
x≠ -3
x≠ 3
Умножим всё уравнение на 3x(3 - x)(x + 3)
(5x + 4)(3 - x) + 3(6 - 7x)(x + 3) = 3x(3x + 1)
15x - 5x²+ 12 - 4x + 3(6x + 18 - 7x² - 21x) = 9x² + 3x
-14x² + 8x + 12 + 3(-7x² - 15x + 18) = 0
-14x² + 8x + 12 - 21x² - 45x + 54 = 0
-35x² - 37x + 66 = 0
35x² + 37x - 66 = 0
D = 37² + 4·66·35 = 10609 = 103²
x₁ = (-37 + 103)/70 = 66/70 = 33/35
x₂ = (-37 - 103)/70 = -140/70 = -2
Ответ: x = -2; 33/5.

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Answer

Answers & Comments

Verified answer

11 yavlyayutsya celym polozhitelnym

(n-2)^2...

(m^2-4))-1...

(3m^2-6m))...

5 3affa118a97a3a2247fe143d6015ae784 8714

primenenie svojstv arifmeticheskogo kvadratnogo kornya vychislite 8125

x 2 k znamenatelyu x 229e0854c6b9ddbcd9810997aa5457b5f0 89670

n...

sokratite drob a3a 5a 5

elochnaya girlyanda sostoit iz 50 lampochek kazhdaya iz kotoryh imeet soprotivlenie 03743b68451c212995fdebe158d9534fb 94221

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