Verified answer

Ответ:

[tex] \frac{3}{x - 2} + \frac{8}{x + 2} = \frac{3}{4} \\ \frac{3(x + 2) + 8(x - 2)}{(x - 2)(x + 2)} = \frac{3}{4} \\ \frac{3x + 6 + 8x - 16}{ {x}^{2} - 4 } = \frac{3}{4} \\ \frac{11x - 10}{ {x}^{2} - 4 } = \frac{3}{4} \\ 44x - 40 = 3 {x}^{2} - 12 \\ 3 {x }^{2} - 44x + 28 = 0 \\ 3{x}^2-42x-2x+28=0\\ 3x(x-14)-2(x-14)=0\\ (x-14)(3x-2)=0\\x-14=0\\x=14\\3x-2=0\\3x=2\\x=\frac{2}{3} [/tex]

Ответ:

Объяснение:

3/(х-2) + 8/(х+2) = 3/4

3 * 4(х+2) + 8 * 4(х-2) = 3(х-2)(х + 2)

12х + 24 + 32х - 64 = 3х² + 6х - 6х - 12

44х - 28 - 3х² = 0

3х² - 44х + 28 = 0

D = 44² - 4 *3 * 28 = 1936 -336 = 1600

√D = √1600 = 40

х₁ = (44 - 40)/2*3 = 2/3

х₂= (44 + 40)/2*3 = 14